AP objective coverage

Required depth: Use the scalar/vector comparison and scaled arrows before calculation; no calculus is needed.

Essential knowledge checked: 1.1.A.1, 1.1.A.2, 1.1.A.3

Study this section → The visible comparison distinguishes magnitude-only quantities from directed quantities; the adjacent scale drawing shows vector magnitude.

Study this section → The component panel resolves a vector with trigonometry and preserves the chosen axes.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Restrict this starting objective to one axis; the later two-axis laboratory is optional here.

Essential knowledge checked: 1.1.B.1

Study this section → Same-direction and opposite-direction addition are explicit; the component laboratory also handles angled vectors.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

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Required depth: Use a signed one-axis coordinate and compare endpoints; explicitly justify replacing an extended object by a point.

Essential knowledge checked: 1.2.A.1, 1.2.A.2

Study this section → The origin, signed coordinate and displacement model are explicit; a particle-model validity discussion is not established here.

Still needed: Add a short decision example for when size and internal motion may be ignored. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

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Required depth: Read average rates and shrinking-interval limits visually; formal differentiation is not required in AP1.

Essential knowledge checked: 1.2.B.1, 1.2.B.2, 1.2.B.3, 1.2.B.4, 1.2.B.5

Study this section → The rate panel compares speed and signed velocity using distance and displacement.

Study this section → The interactive explains acceleration signs by comparison with velocity, rather than equating negative acceleration with slowing.

Study this section → The shrinking-time-interval laboratory provides the average-to-instantaneous bridge; AP1 uses its visual interpretation only.

Study this section → The velocity and acceleration directions are shown together with the radial acceleration magnitude.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Join verbal, graphical and algebraic motion descriptions; calculate constant-acceleration cases and keep nonuniform acceleration qualitative.

Essential knowledge checked: 1.3.A.1, 1.3.A.2, 1.3.A.3, 1.3.A.4

Study this section → Velocity-time slope and signed area are taught together with a changing-motion display.

Study this section → The equation panel restricts the algebraic kinematics equations to constant acceleration.

Study this section → The free-fall section treats constant downward acceleration and the difference between zero velocity and zero acceleration.

Still needed: Add a dedicated nonuniform-acceleration graph comparison without requiring calculus. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

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Required depth: Name both observers before assigning motion; use ordinary inertial frames.

Essential knowledge checked: 1.4.A.1

Study this section → Observer labels, relative velocities and equal accelerations in constant-relative-velocity frames are explicit. The boat example also contains optional two-dimensional material.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use signed velocity addition in one dimension; avoid making the boat laboratory’s two-dimensional geometry compulsory.

Essential knowledge checked: 1.4.B.1, 1.4.B.2

Study this section → Observer labels, relative velocities and equal accelerations in constant-relative-velocity frames are explicit. The boat example also contains optional two-dimensional material.

Study this section → Same-direction and opposite-direction addition are explicit; the component laboratory also handles angled vectors.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Resolve and recombine perpendicular components with trigonometry.

Essential knowledge checked: 1.5.A.1, 1.5.A.2, 1.5.A.3

Study this section → The component panel resolves a vector with trigonometry and preserves the chosen axes.

Study this section → The lesson separates perpendicular motions and reconnects them with a shared time; projectile graphs and horizontal launches follow.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Use a shared time to combine perpendicular motions under the stated acceleration model.

Essential knowledge checked: 1.5.B.1, 1.5.B.2

Study this section → The lesson separates perpendicular motions and reconnects them with a shared time; projectile graphs and horizontal launches follow.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: A system choice must explain which interactions are internal and which transfers cross the boundary.

Essential knowledge checked: 2.1.A.1, 2.1.A.2, 2.1.A.3, 2.1.A.4, 2.1.A.5, 2.1.A.6

Study this section → The diagram rules isolate a system, identify external interactions and choose axes; they do not spell out all College Board drawing conventions.

Study this section → System boundaries, external transfers and conversion into internal energy are explained.

Still needed: Add explicit examples where external interactions alter internal structure, and distinguish a system’s properties from the properties of its parts. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use symmetry or weighted coordinates for up to five point masses in a plane; continuous integrals on the shared page are extension material.

Essential knowledge checked: 2.1.B.1, 2.1.B.2, 2.1.B.3

Study this section → The lesson gives weighted coordinates, the continuous first moment, symmetry, and a composite lamina example.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Identify the interaction partner and whether contact is involved before assigning a force.

Essential knowledge checked: 2.2.A.1, 2.2.A.2

Study this section → The diagram rules isolate a system, identify external interactions and choose axes; they do not spell out all College Board drawing conventions.

Study this section → The interaction-pair examples put each force on a different body.

Study this section → The force library distinguishes weight, applied force and normal contact force.

Still needed: Add the microscopic electric origin of contact forces and an explicit explanation that an object cannot provide its own net external force. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Select axes and draw the actual forces on a dot model; force components belong in the calculation rather than as extra forces.

Essential knowledge checked: 2.2.B.1, 2.2.B.2, 2.2.B.3, 2.2.B.4

Study this section → The diagram rules isolate a system, identify external interactions and choose axes; they do not spell out all College Board drawing conventions.

Study this section → The board adds signed force components independently and connects the resultant to acceleration.

Still needed: Add explicit dot-origin and side-by-side same-direction arrow conventions; the current lesson does not establish every required drawing rule. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Follow equal-and-opposite forces through a cord/system model; use ideal cords and pulleys, with qualitative attention to massive cords.

Essential knowledge checked: 2.3.A.1, 2.3.A.2, 2.3.A.3

Study this section → The interaction-pair examples put each force on a different body.

Study this section → The visible model states equal tension for a massless cord and ideal pulley, and notes that real massive cords can differ.

Study this section → The lesson defines a system/time interval and compares external impulse with cancelling internal impulses.

Still needed: Explain tension through neighbouring cord segments and work through the varying-tension massive-cord case; make the ideal pulley assumptions explicit. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Distinguish zero acceleration from zero speed and balance each direction independently in an inertial frame.

Essential knowledge checked: 2.4.A.1, 2.4.A.2, 2.4.A.3, 2.4.A.4, 2.4.A.5

Study this section → The law selector states constant-velocity equilibrium, proportional acceleration, and equal-and-opposite interaction pairs.

Study this section → The board adds signed force components independently and connects the resultant to acceleration.

Study this section → Observer labels, relative velocities and equal accelerations in constant-relative-velocity frames are explicit. The boat example also contains optional two-dimensional material.

Study this section → The first explanation defines an inertial frame through interaction-free motion and compares constant-velocity frames. The uniform-acceleration paragraph explains a mass-proportional effective gravity; rotating-frame and Coriolis calculations are optional.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Calculate the resultant vector and compare accelerations at different masses; extend the object model to a system’s centre of mass.

Essential knowledge checked: 2.5.A.1, 2.5.A.2, 2.5.A.3

Study this section → The second-law statement and force-acceleration display show the resultant direction and inverse mass dependence.

Study this section → The board adds signed force components independently and connects the resultant to acceleration.

Still needed: The centre-of-mass form for an extended system needs explicit teaching alongside the point-object examples. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Use centre-to-centre separation, distinguish force from field, and interpret field using a small test mass.

Essential knowledge checked: 2.6.A.1, 2.6.A.2, 2.6.A.3

Study this section → The inverse-square model uses centre-to-centre separation, exterior spherical masses, and equal-and-opposite attraction.

Study this section → The gravity applications connect local field strength, weight and orbital free fall; the explicit zero-total-energy argument gives escape speed.

Still needed: Add an explicit gravitational-field test-mass definition and a force-versus-field comparison. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Choose the approximately constant-field model only when height changes are small compared with planetary radius.

Essential knowledge checked: 2.6.B.1, 2.6.B.2

Study this section → The gravity applications connect local field strength, weight and orbital free fall; the explicit zero-total-energy argument gives escape speed.

Study this section → The near-surface and inverse-square energy models are distinguished, including the choice of zero.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Analyze support force separately from gravity; apparent weightlessness is a dynamical condition.

Essential knowledge checked: 2.6.C.1, 2.6.C.2, 2.6.C.3, 2.6.C.4

Study this section → The passenger example identifies the scale reading as normal force and explains free-fall apparent weightlessness.

Study this section → The first explanation defines an inertial frame through interaction-free motion and compares constant-velocity frames. The uniform-acceleration paragraph explains a mass-proportional effective gravity; rotating-frame and Coriolis calculations are optional.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Separate resistance to acceleration from gravitational coupling, then compare their measured equivalence.

Essential knowledge checked: 2.6.D.1, 2.6.D.2, 2.6.D.3

Study this section → The second-law statement and force-acceleration display show the resultant direction and inverse mass dependence.

Study this section → The inverse-square model uses centre-to-centre separation, exterior spherical masses, and equal-and-opposite attraction.

Still needed: The lessons use both meanings but do not explicitly distinguish and experimentally relate inertial and gravitational mass. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use relative sliding to choose direction and the perpendicular normal force in the kinetic-friction law.

Essential knowledge checked: 2.7.A.1, 2.7.A.2

Study this section → Static friction adjusts up to a limit; the kinetic law and relative-sliding direction test are explicit.

Still needed: Add the model’s contact-area independence and a material-pair comparison. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Determine the required static force first, then test its maximum; do not automatically substitute the limiting value.

Essential knowledge checked: 2.7.B.1, 2.7.B.2, 2.7.B.3

Study this section → Static friction adjusts up to a limit; the kinetic law and relative-sliding direction test are explicit.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Measure signed deformation from equilibrium and stay in the ideal linear, negligible-spring-mass model.

Essential knowledge checked: 2.8.A.1, 2.8.A.2, 2.8.A.3

Study this section → Restoring force, signed deformation and the quadratic elastic store are explicitly linked.

Study this section → The extension model and elastic-range qualification teach the linear force law; restoring-force sign is clearer in the elastic-energy lesson.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Resolve radial and tangential effects separately; use the appropriate real-force diagram for turns and vertical circles.

Essential knowledge checked: 2.9.A.1, 2.9.A.2, 2.9.A.3, 2.9.A.4, 2.9.A.5

Study this section → The velocity and acceleration directions are shown together with the radial acceleration magnitude.

Study this section → Real radial forces, friction-limited turning, ideal banking and vertical-circle force signs are taught.

Study this section → The lesson explains lever geometry, signed torque, fixed-axis angular acceleration and constant-angular-acceleration equations.

Still needed: Add conical-pendulum analysis, explicit minimum speed at a loop top, and the qualitative effect of friction on a banked turn. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use circular-orbit gravity and radial acceleration; first/second Kepler-law work is not required for this objective.

Essential knowledge checked: 2.9.B.1

Study this section → The shared astronomy lesson includes circular orbital speed and Kepler scaling among broader astronomy content.

Study this section → The shared section derives the circular-orbit period relation and escape speed; its astronomy/error/black-hole extensions are outside these mechanics objectives.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Compute the scalar motion energy and compare square-speed changes in a named frame.

Essential knowledge checked: 3.1.A.1, 3.1.A.2, 3.1.A.3

Study this section → The scalar kinetic-energy formula and square-speed scaling are explained.

Study this section → Observer labels, relative velocities and equal accelerations in constant-relative-velocity frames are explicit. The boat example also contains optional two-dimensional material.

Still needed: Add an explicit calculation showing that observers assign different kinetic energies to the same object. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Use force-displacement components and signed graphical area; keep the treatment algebraic and mechanical.

Essential knowledge checked: 3.2.A.1, 3.2.A.2, 3.2.A.3, 3.2.A.4, 3.2.A.5

Study this section → The work model makes the system boundary, displacement and force direction explicit.

Study this section → The signed force-displacement area gives work for varying force.

Study this section → The net-work balance converts initial and final kinetic energies into a speed calculation.

Study this section → The near-surface and inverse-square energy models are distinguished, including the choice of zero.

Study this section → System boundaries, external transfers and conversion into internal energy are explained.

Study this section → The model builds the dot-product path integral and compares conservative gravity with path-dependent friction. C Mechanics can use the calculus; AP Physics 1 uses only the constant-gravity and constant-friction path comparison, including a closed loop.

Still needed: The conservative closed-path comparison is taught. Add the distinction between displacement of the force application point and displacement of the centre of mass. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Choose the system and energy zero before combining spring, near-surface and inverse-square models.

Essential knowledge checked: 3.3.A.1, 3.3.A.2, 3.3.A.3, 3.3.A.4, 3.3.A.5

Study this section → The near-surface and inverse-square energy models are distinguished, including the choice of zero.

Study this section → Restoring force, signed deformation and the quadratic elastic store are explicitly linked.

Study this section → System boundaries, external transfers and conversion into internal energy are explained.

Still needed: Teach pairwise potential-energy addition for more than two objects and make the interaction/system ownership of potential energy explicit. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: A useful energy account depends on which interacting objects lie inside the chosen boundary.

Essential knowledge checked: 3.4.A.1, 3.4.A.2

Study this section → System boundaries, external transfers and conversion into internal energy are explained.

Still needed: Add a direct single-particle-versus-interacting-system comparison; the broad energy-store list does not establish the mechanical system distinction. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Balance mechanical stores with external transfers and internal dissipation; thermal and sound conversion should be named where relevant.

Essential knowledge checked: 3.4.B.1, 3.4.B.2, 3.4.B.3, 3.4.B.4

Study this section → System boundaries, external transfers and conversion into internal energy are explained.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Revisit the same process with different boundaries before deciding whether mechanical energy is constant.

Essential knowledge checked: 3.4.C.1, 3.4.C.2, 3.4.C.3

Study this section → System boundaries, external transfers and conversion into internal energy are explained.

Study this section → The work model makes the system boundary, displacement and force direction explicit.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Compare energy per time with the force component along instantaneous velocity; use algebra.

Essential knowledge checked: 3.5.A.1, 3.5.A.2, 3.5.A.3, 3.5.A.4

Study this section → The formula panel compares average transfer rate with instantaneous force-velocity power.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use signed/vector momentum and identify whether a short collision or an explosion can be treated as an internal interaction.

Essential knowledge checked: 4.1.A.1, 4.1.A.2, 4.1.A.3

Study this section → Signed momentum and vector addition for a system are explicit.

Study this section → The lesson defines a system/time interval and compares external impulse with cancelling internal impulses.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Read force-time area and momentum-time slope without requiring formal calculus.

Essential knowledge checked: 4.2.A.1, 4.2.A.2, 4.2.A.3, 4.2.A.4, 4.2.A.5

Study this section → The average-force model, signed force-time area and rebound momentum change are taught.

Study this section → Force is read as momentum-time slope and integrated over time; the variable-mass wording needs the separate system-balance qualification.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Relate the net impulse to final-minus-initial momentum and obtain the constant-mass second-law case; quantitative variable mass is outside AP1.

Essential knowledge checked: 4.2.B.1, 4.2.B.2, 4.2.B.3

Study this section → The average-force model, signed force-time area and rebound momentum change are taught.

Study this section → Force is read as momentum-time slope and integrated over time; the variable-mass wording needs the separate system-balance qualification.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Calculate one-dimensional collisions; two-dimensional component setups and qualitative/semiquantitative reasoning suffice without solving coupled equations.

Essential knowledge checked: 4.3.A.1, 4.3.A.2, 4.3.A.3, 4.3.A.4

Study this section → The lesson defines a system/time interval and compares external impulse with cancelling internal impulses.

Study this section → The lesson compares elastic and inelastic collisions, centre-of-mass motion and energy conversion.

Study this section → The worked method conserves each perpendicular momentum component before recombining velocity.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: State the chosen system and external impulse before claiming constant momentum.

Essential knowledge checked: 4.3.B.1, 4.3.B.2, 4.3.B.3

Study this section → The lesson defines a system/time interval and compares external impulse with cancelling internal impulses.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Compare total kinetic energy, individual velocities and the sticking limit; momentum and kinetic-energy conservation are separate tests.

Essential knowledge checked: 4.4.A.1, 4.4.A.2, 4.4.A.3, 4.4.A.4, 4.4.A.5

Study this section → The lesson compares elastic and inelastic collisions, centre-of-mass motion and energy conversion.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Use radians, signed clockwise/counterclockwise motion and constant-angular-acceleration algebra; numerical calculus is unnecessary.

Essential knowledge checked: 5.1.A.1, 5.1.A.2, 5.1.A.3, 5.1.A.4

Study this section → The lesson connects radians, period, frequency, arc length and tangential speed.

Study this section → The lesson explains lever geometry, signed torque, fixed-axis angular acceleration and constant-angular-acceleration equations.

Still needed: Add coordinated angular position/velocity/acceleration graphs at AP1 level and explicit rigid-system versus point-object modeling. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Connect arc length, tangential speed and tangential acceleration at a chosen radius; recognize the common angular rates of a rigid body.

Essential knowledge checked: 5.2.A.1, 5.2.A.2, 5.2.A.3

Study this section → The lesson connects radians, period, frequency, arc length and tangential speed.

Study this section → The lesson explains lever geometry, signed torque, fixed-axis angular acceleration and constant-angular-acceleration equations.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Locate the axis, the force line and the perpendicular lever arm before assigning a torque.

Essential knowledge checked: 5.3.A.1, 5.3.A.2

Study this section → The lesson explains lever geometry, signed torque, fixed-axis angular acceleration and constant-angular-acceleration equations.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Keep the force’s application point on the extended object and calculate the signed turning effect in one plane.

Essential knowledge checked: 5.3.B.1, 5.3.B.2

Study this section → The lesson explains lever geometry, signed torque, fixed-axis angular acceleration and constant-angular-acceleration equations.

Study this section → Separate force and moment equations distinguish translational and rotational balance.

Still needed: Add an explicit comparison of extended-object force diagrams with point-model free-body diagrams. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Sum up to five planar point-mass contributions; use supplied extended-body inertia expressions rather than calculus derivations.

Essential knowledge checked: 5.4.A.1, 5.4.A.2, 5.4.A.3

Study this section → Discrete sums, the continuous integral, mass-distribution comparisons and parallel-axis shifts are presented.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Use a parallel shift from the centre-of-mass axis and explain why that axis gives the minimum inertia among parallel axes.

Essential knowledge checked: 5.4.B.1, 5.4.B.2

Study this section → Discrete sums, the continuous integral, mass-distribution comparisons and parallel-axis shifts are presented.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Balance torques in one plane and distinguish constant angular velocity from rest and from translational equilibrium.

Essential knowledge checked: 5.5.A.1, 5.5.A.2

Study this section → Separate force and moment equations distinguish translational and rotational balance.

Study this section → The lesson explains lever geometry, signed torque, fixed-axis angular acceleration and constant-angular-acceleration equations.

Still needed: The current equilibrium examples focus on rest; add contrasting cases with constant rotation or translational acceleration. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Use fixed-axis inertia and net torque, then combine with an independent translational equation when required.

Essential knowledge checked: 5.6.A.1, 5.6.A.2, 5.6.A.3

Study this section → The lesson explains lever geometry, signed torque, fixed-axis angular acceleration and constant-angular-acceleration equations.

Study this section → The no-slip constraints, instantaneous contact rest and split translational/rotational energy are taught.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Compare a rigid body’s spin energy with its centre-of-mass translation; do not double-count a point particle’s energy.

Essential knowledge checked: 6.1.A.1, 6.1.A.2, 6.1.A.3

Study this section → Rotational energy and torque-angle work area are explicit; the panel also states the variable-torque integral.

Study this section → The no-slip constraints, instantaneous contact rest and split translational/rotational energy are taught.

Still needed: Add the explicit point-particle equivalence between orbital rotational energy and its translational kinetic energy. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Use constant-torque multiplication or signed torque-angle area; the integral notation on the shared page is optional for AP1.

Essential knowledge checked: 6.2.A.1, 6.2.A.2, 6.2.A.3

Study this section → Rotational energy and torque-angle work area are explicit; the panel also states the variable-torque integral.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use rigid-body angular momentum and the perpendicular particle momentum component, including straight-line motion about an offset origin.

Essential knowledge checked: 6.3.A.1, 6.3.A.2

Study this section → The particle cross product, origin dependence, rigid-body angular momentum and torque rate are stated.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use average torque over a time interval and signed torque-time area; attach the rotational sense consistently.

Essential knowledge checked: 6.3.B.1, 6.3.B.2, 6.3.B.3

Study this section → The particle cross product, origin dependence, rigid-body angular momentum and torque rate are stated.

Still needed: The torque-rate relation is present, but the angular-impulse quantity, finite-interval relation and torque-time area need explicit teaching. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Connect finite angular-momentum change to torque-time area and read torque from an angular-momentum graph slope.

Essential knowledge checked: 6.3.C.1, 6.3.C.2, 6.3.C.3, 6.3.C.4

Study this section → The particle cross product, origin dependence, rigid-body angular momentum and torque rate are stated.

Study this section → Differentiation and integration link angular kinematics; the dynamics extension gives torque as the angular-momentum rate.

Still needed: Add the angular impulse theorem, a torque-time graph and an angular-momentum-time graph; the derivative statement alone does not cover all representations. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Add constituent angular momenta about one common axis and analyze changing inertia without confusing energy conservation.

Essential knowledge checked: 6.4.A.1, 6.4.A.2

Study this section → Zero external torque, changing inertia and internal work are illustrated by rotating systems and central forces.

Study this section → The particle cross product, origin dependence, rigid-body angular momentum and torque rate are stated.

Still needed: Add an explicit internal equal-and-opposite angular-impulse account between the interacting constituents. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: State the axis and system before deciding whether an external torque can change angular momentum.

Essential knowledge checked: 6.4.B.1, 6.4.B.2, 6.4.B.3

Study this section → The particle cross product, origin dependence, rigid-body angular momentum and torque rate are stated.

Study this section → Zero external torque, changing inertia and internal work are illustrated by rotating systems and central forces.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use the centre-of-mass translational term and the spin term about the centre of mass.

Essential knowledge checked: 6.5.A.1

Study this section → The no-slip constraints, instantaneous contact rest and split translational/rotational energy are taught.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Use no-slip speed/acceleration links and distinguish static contact from dissipative sliding.

Essential knowledge checked: 6.5.B.1, 6.5.B.2

Study this section → The no-slip constraints, instantaneous contact rest and split translational/rotational energy are taught.

Still needed: The lesson gives instantaneous contact rest but should explicitly state why ideal static friction does not dissipate mechanical energy. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Keep AP1 slipping analysis qualitative; quantitative slipping and rolling resistance are beyond this course scope.

Essential knowledge checked: 6.5.C.1, 6.5.C.2

Still needed: Add a slipping-wheel lesson distinguishing independent translation/rotation and dissipative kinetic friction. No matching canonical practice was verified.

No practice question has yet been verified for this objective.

Required depth: Apply energy and angular-momentum accounts to a negligible-mass satellite around a dominant central mass; distinguish circular from elliptical motion.

Essential knowledge checked: 6.6.A.1, 6.6.A.2, 6.6.A.3

Study this section → The near-surface and inverse-square energy models are distinguished, including the choice of zero.

Study this section → Zero external torque, changing inertia and internal work are illustrated by rotating systems and central forces.

Study this section → The gravity applications connect local field strength, weight and orbital free fall; the explicit zero-total-energy argument gives escape speed.

Still needed: Add an integrated circular/elliptical energy account and the circular total-energy relation. The gravity applications already explain the zero-energy escape condition. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Identify proportional restoring force or torque rather than treating all periodic motion as SHM.

Essential knowledge checked: 7.1.A.1, 7.1.A.2

Study this section → The AP-visible generic lesson defines restoring acceleration, period models, phase relationships and amplitude independence.

Study this section → The simple-pendulum paragraphs derive the restoring torque and identify the small-angle limit. The next paragraph constructs a physical pendulum with the parallel-axis theorem. AP Physics 1 needs the simple-pendulum argument only; physical pendulums and amplitude-series corrections are optional there.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use spring parameters or a small-angle pendulum length; interpret parameter changes and the period/frequency conversion.

Essential knowledge checked: 7.2.A.1

Study this section → The AP-visible generic lesson defines restoring acceleration, period models, phase relationships and amplitude independence.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Read displacement, velocity and acceleration phase/extrema from sinusoidal motion; use algebraic time functions rather than differential-equation proofs.

Essential knowledge checked: 7.3.A.1, 7.3.A.2, 7.3.A.3

Study this section → The AP-visible generic lesson defines restoring acceleration, period models, phase relationships and amplitude independence.

Study this section → The undamped energy budget, displacement and time graphs, and amplitude-squared scaling are taught.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Connect total energy to amplitude and compare the kinetic/potential split at positions and times.

Essential knowledge checked: 7.4.A.1, 7.4.A.2, 7.4.A.3, 7.4.A.4

Study this section → The undamped energy budget, displacement and time graphs, and amplitude-squared scaling are taught.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Distinguish the particle/state model from the ideal assumptions used in fluid calculations.

Essential knowledge checked: 8.1.A.1, 8.1.A.2, 8.1.A.3, 8.1.A.4

Study this section → The routed custom lesson distinguishes states of matter with particle motion; its density calculator provides the mass-volume relationship.

Study this section → Density and relative-density calculations are taught in the actual MatterChapterLesson template.

Study this section → The visible formula panel includes hydrostatics, absolute pressure, volume flow, continuity and Bernoulli under stated ideal-flow assumptions.

Still needed: Make the fluid definition and incompressible/nonviscous model assumptions explicit beside the states-of-matter introduction. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Treat pressure as scalar and distinguish it from the normal force on a chosen area; use a constant-density liquid model where appropriate.

Essential knowledge checked: 8.2.A.1, 8.2.A.2, 8.2.A.3

Study this section → The force-per-area model and perpendicular contact force support pressure calculations.

Study this section → The visible explanation treats scalar pressure and a pressure gradient as the cause of fluid acceleration.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Distinguish absolute pressure from an added hydrostatic/gauge contribution and link pressure to particle interactions.

Essential knowledge checked: 8.2.B.1, 8.2.B.2, 8.2.B.3

Study this section → The visible formula panel includes hydrostatics, absolute pressure, volume flow, continuity and Bernoulli under stated ideal-flow assumptions.

Still needed: Add the microscopic origin of fluid pressure alongside the hydrostatic treatment. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Apply force balance and acceleration to a fluid element, not only to a solid submerged in fluid.

Essential knowledge checked: 8.3.A.1, 8.3.A.2

Study this section → The visible explanation treats scalar pressure and a pressure gradient as the cause of fluid acceleration.

Still needed: The pressure-gradient explanation is a start; add particle/element force diagrams and the connection from collective interactions to the fluid’s motion. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use pressure differences to explain the upward resultant, then compare it with weight and displaced-fluid mass; calculus on the supplemental section is optional.

Essential knowledge checked: 8.3.B.1, 8.3.B.2, 8.3.B.3

Study this section → The displaced-fluid model, float/sink force comparison and density ratio are taught.

Study this section → The pressure-difference derivation of buoyancy is explicit for a prism, with the surface integral identified for other shapes.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Relate volume and mass flow to section area and speed in steady full-pipe flow; pressure differences drive changes in motion.

Essential knowledge checked: 8.4.A.1, 8.4.A.2

Study this section → The visible formula panel includes hydrostatics, absolute pressure, volume flow, continuity and Bernoulli under stated ideal-flow assumptions.

Study this section → The visible explanation treats scalar pressure and a pressure gradient as the cause of fluid acceleration.

Still needed: Add an explicit mass-flow rate treatment and a derivation from mass conservation. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Apply the ideal streamline energy model with pressure, height and speed terms; make all assumptions visible.

Essential knowledge checked: 8.4.B.1, 8.4.B.2, 8.4.B.3

Study this section → The visible formula panel includes hydrostatics, absolute pressure, volume flow, continuity and Bernoulli under stated ideal-flow assumptions.

Study this section → Worked example 07 uses equal atmospheric pressures to derive the efflux speed, then keeps the height term to find pressure at a raised crest. This fills the unequal-height Bernoulli case; later Reynolds-number analysis and the vapour-pressure limit are optional. This lesson example is not a canonical bank item.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Connect momentum transfer and perpendicular force per area to gas pressure throughout the gas; collision reasoning is limited to one or two dimensions.

Essential knowledge checked: 9.1.A.1

Study this section → The kinetic explanation links elastic wall collisions, momentum reversal and force per area.

Still needed: Wall pressure is explained, but pressure throughout the gas and a quantitative oblique-collision component example are not established in the inspected explanation. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Relate mean molecular kinetic energy and RMS speed to absolute temperature; read distribution shape changes without memorizing its functional form.

Essential knowledge checked: 9.1.B.1

Study this section → The model relates temperature to mean translational kinetic energy.

Study this section → RMS-speed equations and the discussion of the distribution peak, tail and temperature changes are present.

Still needed: No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use both particle-count and molar gas laws, model assumptions, state-variable graphs and idealized zero-pressure extrapolation; algebra only.

Essential knowledge checked: 9.2.A.1, 9.2.A.2, 9.2.A.3, 9.2.A.4

Study this section → The negligible-size, random-motion and elastic-collision assumptions are explicitly stated.

Study this section → The gas-law explanation and graph descriptions connect pressure, volume, amount and temperature.

Study this section → The ideal-gas extrapolation explicitly distinguishes the mathematical limit from real-gas condensation.

Practise this objective →

Required depth: Explain transfer direction and conduction, convection and radiation, including microscopic exchange and the meaning of no net transfer; qualitative.

Essential knowledge checked: 9.3.A.1, 9.3.A.2, 9.3.A.3, 9.3.A.4

Study this section → Temperature, heat transfer and equal-temperature equilibrium are distinguished.

Study this section → The three transfer mechanisms and molecular conduction are explained.

Still needed: The inspected discussion does not develop the many-collision probability argument that leads interacting systems toward a common temperature.

Practise this objective →

Required depth: Distinguish microscopic kinetic/potential energy from centre-of-mass motion; use U=3nRT/2 for a monatomic ideal gas.

Essential knowledge checked: 9.4.A.1, 9.4.A.2

Study this section → The definition distinguishes microscopic kinetic and potential energy.

Study this section → The challenging example distinguishes translational energy from full internal energy and restricts the monatomic result.

Still needed: The centre-of-mass versus internal-energy distinction is not explicitly developed in the inspected passages.

Practise this objective →

Required depth: Track heat and work with an explicit sign convention, read PV areas and identify constant-P/V/T and adiabatic processes; no calculus required.

Essential knowledge checked: 9.4.B.1, 9.4.B.2, 9.4.B.3

Study this section → The first-law explanation, process shapes and PV area calculation are present. The page uses work done BY the gas, so translate to the AP work-ON convention before combining signs.

Practise this objective →

Required depth: Use temperature-independent specific heat and conservation of energy; connect the material property to microscopic structure.

Essential knowledge checked: 9.5.A.1, 9.5.A.2

Study this section → Specific heat and insulated-mixture energy balance are explained and calculated.

Still needed: The material dependence of specific heat is used but not connected explicitly to microscopic arrangement and interactions.

Practise this objective →

Required depth: Use thickness, cross-sectional area, temperature difference and conductivity to compare heat-flow rates; treat material conductivity as an intrinsic property.

Essential knowledge checked: 9.5.B.1, 9.5.B.2

Study this section → The conduction formula and lattice/electron explanation connect geometry, thermal gradient and material response.

Still needed: No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Reason qualitatively about entropy, equilibrium, reversibility and isolated versus exchanging systems; entropy calculations are outside the AP2 requirement.

Essential knowledge checked: 9.6.A.1, 9.6.A.2, 9.6.A.3

Study this section → The spreading-energy explanation and hot/cold exchange example support the direction of total entropy change; logarithms and entropy calculations are enrichment.

Study this section → The free-expansion example explicitly identifies entropy as a state function. Only that qualitative interpretation is required here, not its logarithmic calculation.

Still needed: The explanation needs an explicit maximum-at-equilibrium condition and a closed-system versus isolated-system comparison. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use quantized charge, the point-charge model and Coulomb force; at most four interacting objects unless symmetry simplifies the system, and connect contact forces to electric interactions.

Essential knowledge checked: 10.1.A.1, 10.1.A.2, 10.1.A.3, 10.1.A.4

Study this section → Charge sign, quantization and electron-transfer accounting are explained.

Study this section → Magnitude, inverse-square scaling and the line-of-centres direction are taught.

Study this section → The force-component method supports several point charges.

Still needed: The inspected electrostatics lessons do not explain the electric origin of macroscopic normal force, friction and tension.

Practise this objective →

Required depth: Compare attraction/repulsion and relative interaction strengths, then explain why near-neutral large systems are often gravity-dominated; algebraic ratios.

Essential knowledge checked: 10.1.B.1, 10.1.B.2, 10.1.B.3

Study this section → A worked proton/electron example compares electric and gravitational force magnitudes.

Still needed: The route teaches the force ratio, but the large-scale neutrality explanation occurs in separate presentation extras rather than the inspected lesson body, and is not credited here. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Relate polarization and charge mobility to material permittivity; distinguish vacuum permittivity from the response of matter without microscopic calculations.

Essential knowledge checked: 10.1.C.1, 10.1.C.2, 10.1.C.3, 10.1.C.4

Study this section → Bound-charge polarization and mobile-charge redistribution are contrasted.

Study this section → The capacitor model uses relative permittivity as a material factor.

Still needed: The lesson does not explicitly define permittivity as a measure of polarization response or connect it to how readily electrons change configuration. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Explain friction/contact, induction, grounding and charge redistribution with a defined system boundary; conserve net charge for isolated systems.

Essential knowledge checked: 10.2.A.1, 10.2.A.2, 10.2.A.3

Study this section → The charge ledger makes transfers equal and opposite.

Study this section → The grounded-induction sequence and equal-potential contact condition are explained.

Study this section → Neutral polarization is distinguished from acquiring net charge.

Still needed: No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use force per test charge, field vectors and superposition; calculations involve at most four sources except symmetric configurations.

Essential knowledge checked: 10.3.A.1, 10.3.A.2, 10.3.A.3

Study this section → The test charge is explicitly small enough not to disturb the source field.

Study this section → The explanation interprets tangent direction and relative line density.

Study this section → Vector addition and null-region reasoning are taught.

Practise this objective →

Required depth: Explain conducting equilibrium and spherically symmetric exterior fields; analyze insulator interiors qualitatively only.

Essential knowledge checked: 10.3.B.1, 10.3.B.2

Study this section → Zero field within conducting material, surface charge and normal surface fields are explicit.

Study this section → The exterior spherical-distribution equivalence is stated.

Study this section → The insulator model explains bound charge and local polarization.

Still needed: An explicit comparison of volume-distributed insulator charge and a potentially nonzero interior field is missing from the inspected explanation.

Practise this objective →

Required depth: Use a declared zero at infinity, signed pair energies and the sum over distinct charge pairs; at most four point charges, no extended-distribution integration.

Essential knowledge checked: 10.4.A.1, 10.4.A.2, 10.4.A.3

Study this section → The pair-energy expression and distinction between field work and slow external work are taught.

Study this section → The three-charge example counts the three distinct pairs, adds their energies and interprets the assembly work from infinity.

Practise this objective →

Required depth: Calculate signed scalar potential and energy per charge, including batteries and connected conductors; at most four charges unless symmetry applies.

Essential knowledge checked: 10.5.A.1, 10.5.A.2, 10.5.A.3, 10.5.A.4

Study this section → Potential, potential difference and signed energy changes are distinguished.

Study this section → Signed scalar summation and contrast with zero field are taught.

Study this section → Connected conductors are explicitly described as reaching equal potential.

Study this section → The supply transfers energy to charge and components transfer it out.

Practise this objective →

Required depth: Read field direction, strength and perpendicularity from potential maps; use finite potential differences over distance, with derivatives treated as enrichment.

Essential knowledge checked: 10.5.B.1, 10.5.B.2

Study this section → The explanation links spacing, field direction, perpendicular lines and zero work along an equipotential.

Study this section → The uniform-field expression supplies an algebraic finite-difference case.

Practise this objective →

Required depth: Relate geometry, dielectric, charge, voltage, stored energy and uniform-field motion; parallel plates only, ignoring edges unless specified.

Essential knowledge checked: 10.6.A.1, 10.6.A.2, 10.6.A.3, 10.6.A.4, 10.6.A.5, 10.6.A.6

Study this section → Geometry-dependent capacitance, equal/opposite plate charge and stored energy are present.

Study this section → The uniform-field lesson treats the charged-particle trajectory using constant acceleration.

Still needed: The dielectric is treated as a capacitance multiplier; its induced field opposing the original plate field is not explained explicitly.

Practise this objective →

Required depth: Use signed charge times potential difference and conservation of energy to connect potential-energy changes with kinetic energy; algebra.

Essential knowledge checked: 10.7.A.1, 10.7.A.2

Study this section → Electric work and signed configuration-energy changes are explained.

Study this section → The voltage model connects potential difference to energy.

Study this section → The electron-acceleration example explicitly converts charge times voltage to kinetic energy and solves for speed.

Still needed: No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Relate charge flow to time, distinguish random motion from drift, and use conventional direction while recognizing current is not a spatial vector.

Essential knowledge checked: 11.1.A.1, 11.1.A.2

Study this section → The actual CircuitLessonTemplate renders the random-motion, applied-voltage and conventional-current explanations.

Still needed: The inspected explanation does not explicitly distinguish directed circuit current from a vector quantity. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Interpret connected paths, shared elements, open/closed/short circuits and common or variable symbols; diagrams use conventional current.

Essential knowledge checked: 11.2.A.1, 11.2.A.2, 11.2.A.3, 11.2.A.4

Study this section → The rendered circuit template includes symbol explanations, a symbol guide and closed-path reasoning.

Study this section → The short-circuit current example supports the low-external-resistance case.

Still needed: Shared elements in multiple loops and the zero-potential-drop meaning of a short circuit are not explicitly connected in the inspected explanation.

Practise this objective →

Required depth: Use uniform-specimen geometry and material resistivity, including the usual temperature trend of conductors; algebra and area conversion.

Essential knowledge checked: 11.3.A.1, 11.3.A.2

Study this section → The actual template renders resistance scaling, scattering and the temperature dependence of metal resistivity.

Still needed: No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use V=IR, I–V gradient and electrical heating; identify an ideal ohmic model and state its physical assumptions.

Essential knowledge checked: 11.3.B.1

Study this section → The page defines static resistance, straight I–V behavior and reciprocal graph gradient.

Study this section → Energy conversion in a resistive element is explained.

Still needed: The CED’s ideal-ohmic resistivity convention must be distinguished from the page’s fixed-temperature real-metal treatment; no explicit reconciliation is provided. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use power and its resistor forms to track energy transfer and compare bulb brightness under stated assumptions; algebra.

Essential knowledge checked: 11.4.A.1, 11.4.A.2

Study this section → Power relations and resistive heating are explained.

Still needed: The power explanation lacks an explicit brightness-versus-power account; the circuit-builder colors are explicitly not calibrated brightness.

Practise this objective →

Required depth: Recognize series and parallel topology, shared current or voltage, and equivalent-resistance changes; nested combinations by algebra.

Essential knowledge checked: 11.5.A.1, 11.5.A.2

Study this section → The template renders the reason current/voltage are shared.

Study this section → The actual template places the series sum and reciprocal parallel sum in its formula toolkit.

Practise this objective →

Required depth: Model battery internal resistance in series and wire resistance when significant; ideal components by default, no unequal-voltage parallel batteries.

Essential knowledge checked: 11.5.B.1, 11.5.B.2, 11.5.B.3

Study this section → Open-circuit emf, terminal voltage and the internal series-resistance model are taught.

Study this section → Wire resistance can be calculated from material and geometry.

Still needed: The inspected routes do not explicitly explain when wire resistance can be neglected relative to other elements and why it cannot be dropped in a wire-only loop.

Practise this objective →

Required depth: Place ammeters in series and voltmeters in parallel; use ideal resistances and discuss nonideal loading qualitatively only.

Essential knowledge checked: 11.5.C.1, 11.5.C.2, 11.5.C.3

Study this section → The actual template’s formula toolkit states ideal meter resistances and placement.

Study this section → The loaded-divider worked example shows how a finite voltmeter resistance changes the circuit.

Still needed: Finite-voltmeter loading is demonstrated, but the corresponding qualitative effect of a nonzero ammeter resistance is not developed explicitly. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Apply signed potential changes around a loop and represent potential versus position; algebraic loop equations rather than calculus.

Essential knowledge checked: 11.6.A.1, 11.6.A.2, 11.6.A.3, 11.6.A.4

Study this section → The loop law is tied to energy conservation, sign choices and simultaneous equations.

Study this section → Source gains and component drops are explained as energy per charge.

Still needed: A potential-versus-position graph around a complete loop is not supplied in the inspected lesson content. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Apply conservation of charge to directed branch currents and interpret signed unknowns; algebra.

Essential knowledge checked: 11.7.A.1, 11.7.A.2

Study this section → The junction equation is explicitly derived from charge not accumulating or disappearing.

Practise this objective →

Required depth: Combine series and parallel capacitances and explain equal series-plate charge using conservation; algebra.

Essential knowledge checked: 11.8.A.1, 11.8.A.2

Study this section → The explanation derives both equivalent-capacitance rules from charge and potential constraints.

Study this section → The series example explicitly obtains a combined capacitance below the smaller component, equal plate-charge magnitudes and voltages adding to the supply.

Still needed: No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Explain charging/discharging shapes and time-constant meaning; calculate initial/final states only, with no time-dependent mathematical model required.

Essential knowledge checked: 11.8.B.1, 11.8.B.2

Study this section → The discharge model supplies qualitative decay and the time constant. Differential equations and exponential-time calculations on the page are enrichment.

Still needed: A full qualitative charging sequence, initially wire-like behavior and the long-time branch model are not taught together. The shared page emphasizes out-of-scope calculus and discharge. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Interpret magnetic vector fields, dipoles and closed field lines; qualitative field maps.

Essential knowledge checked: 12.1.A.1, 12.1.A.2

Study this section → Dipole poles, closed loops and the response of magnets or moving charges are explained.

Still needed: No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use dipole alignment to explain permanent/induced magnetism, Earth’s approximate dipole field and ferro-, para- and diamagnetic responses; qualitative.

Essential knowledge checked: 12.1.B.1, 12.1.B.2, 12.1.B.3, 12.1.B4

Study this section → The lesson supports pole pairing, ferromagnetic domains, compass alignment and Earth’s field.

Still needed: Paramagnetic and diamagnetic behavior, orbital/spin origins and explicit Earth-as-dipole modeling are not developed. The source prints the final EK label as 12.1.B4; that spelling is retained. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Distinguish vacuum permeability and material magnetization response, including dependence on conditions; qualitative material reasoning.

Essential knowledge checked: 12.1.C.1, 12.1.C.2, 12.1.C.3

Study this section → The worked solenoid/core example uses vacuum and relative permeability as field factors.

Still needed: The numerical multiplier does not explain permeability as a response measure or its variation with temperature, orientation and applied field. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Describe how field direction and strength depend on a single charge’s velocity and observation direction; qualitative vector geometry.

Essential knowledge checked: 12.2.A.1

Still needed: The inspected magnetism routes start with current-carrying wires and force on a moving charge; no standalone field-of-one-moving-charge explanation was verified. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Combine electric and magnetic forces and explain Hall separation; numerical magnetic-force angles are restricted to 0°,90°,180°, other angles qualitative.

Essential knowledge checked: 12.2.B.1, 12.2.B.2, 12.2.B.3, 12.2.B.4

Study this section → The force direction, no-work result and crossed-field selector are explained.

Study this section → The Hall paragraph explains transverse carrier displacement and electric/magnetic balance; Ampère-law material elsewhere is enrichment.

Practise this objective →

Required depth: Use the long-wire inverse-distance field, loop direction and vector superposition of wire fields; algebra and right-hand reasoning.

Essential knowledge checked: 12.3.A.1

Study this section → The circular wire pattern, inverse-distance law and loop direction are taught.

Study this section → The advanced route explains combining wire fields; line-integral derivations are not required.

Still needed: No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Relate force to field, current, immersed length and orientation, including direction; algebra and trigonometry.

Essential knowledge checked: 12.3.B.1

Study this section → The force relation, direction, opposite currents and motor example are explained.

Practise this objective →

Required depth: Use oriented area, signed flux, finite flux-change rates, Lenz direction and moving-rod emf; no calculus derivation required.

Essential knowledge checked: 12.4.A.1, 12.4.A.2, 12.4.A.3, 12.4.A.4, 12.4.A.5

Study this section → The normal-angle convention and area/field/orientation changes are taught.

Study this section → Finite-change Faraday law, graph gradients and motional emf are given.

Study this section → The induced-field direction is tied to opposition and energy conservation.

Still needed: The flux explanation focuses on magnitude and does not explicitly establish the signed parallel/antiparallel area-vector convention. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Relate rays and wavefronts, trace paths through interactions, and identify when diffraction prevents a purely ray description; qualitative geometry.

Essential knowledge checked: 13.1.A.1, 13.1.A.2

Study this section → Ray direction, wavefront perpendicularity, shadows and the wavelength-dependent limit of ray optics are given.

Still needed: A laser as a coherent monochromatic ray source is not explicitly identified in this inspected ray-model explanation. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Apply equal normal-referenced angles and explain specular versus diffuse reflection through surface normals; geometry.

Essential knowledge checked: 13.1.B.1, 13.1.B.2, 13.1.B.3, 13.1.B.4

Study this section → The normal convention and smooth/rough-surface distinction are explicitly taught.

Still needed: No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use rays, signed image/focal distances and magnification for plane, concave and convex spherical mirrors; paraxial geometry and algebra.

Essential knowledge checked: 13.2.A.1, 13.2.A.2, 13.2.A.3, 13.2.A.4, 13.2.A.5, 13.2.A.6, 13.2.A.7, 13.2.A.8, 13.2.A.9

Study this section → Plane-mirror image location and virtual-ray interpretation are given.

Study this section → Curved-mirror equations, image cases and principal rays are explained.

Still needed: The plane-mirror infinite focal length and the principal ray reflecting at the mirror vertex are not explicitly developed. The curved lesson substitutes a centre-of-curvature ray. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use refractive index, normal-referenced Snell geometry, critical angle and total internal reflection; algebra and trigonometry.

Essential knowledge checked: 13.3.A.1, 13.3.A.2, 13.3.A.3, 13.3.A.4, 13.3.A.5

Study this section → The explanation connects changed wave speed, unchanged frequency and bending.

Study this section → Critical-angle geometry and the high-to-low-index condition are explicit.

Practise this objective →

Required depth: Use signed thin-lens and magnification relations plus ray diagrams for converging/diverging lenses; distinguish real and virtual images.

Essential knowledge checked: 13.4.A.1, 13.4.A.2, 13.4.A.3, 13.4.A.4, 13.4.A.5, 13.4.A.6, 13.4.A.7

Study this section → The model, principal-ray rules and image cases are taught.

Practise this objective →

Required depth: Distinguish pulse/wave, mechanical/EM and transverse/longitudinal behavior; relate medium properties, string tension/density, sound temperature and amplitude to propagation.

Essential knowledge checked: 14.1.A.1, 14.1.A.2, 14.1.A.3, 14.1.A.4, 14.1.A.5, 14.1.A.6

Study this section → The wave template explains energy transfer, transverse/longitudinal motion and displacement graphs.

Study this section → The sound description links compressions, rarefactions, loudness and amplitude.

Still needed: The inspected routes do not fully develop single pulses, the string-speed tension/linear-density law, temperature-dependent sound speed and pressure-amplitude interpretation. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Relate period, frequency, wavelength, speed and sinusoidal time/position graphs; distinguish amplitude, pitch and frequency-dependent energy.

Essential knowledge checked: 14.2.A.1, 14.2.A.2, 14.2.A.3

Study this section → The actual wave template presents period/wavelength graphs and v=fλ.

Study this section → The sinusoidal displacement expression can support the time graph; differentiating it is enrichment.

Still needed: An explicit sinusoidal position equation and the stated amplitude/frequency independence and energy-frequency comparison are not fully taught in the selected sections. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Explain reflected/transmitted wave phase, frequency conservation, transverse polarization and power per area; use qualitative boundary reasoning.

Essential knowledge checked: 14.3.A.1, 14.3.A.2, 14.3.A.3

Study this section → The fixed-end reflection explanation supports one inversion case.

Study this section → Frequency continuity at a boundary is stated.

Study this section → Transverse polarization and attenuation by polarizers are explained; Malus calculations exceed the specific qualitative requirement.

Still needed: Reflection at transitions to slower/faster media and the full intensity-as-average-power-per-area definition are not developed together. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Explain transverse mutually perpendicular fields, vacuum propagation and spectrum/visible-color ordering; exact wavelength band limits are not required.

Essential knowledge checked: 14.4.A.1, 14.4.A.2, 14.4.A.3

Study this section → The field orientation, no-medium property and band ordering are present.

Study this section → Dispersion and color separation provide supporting visible-spectrum context.

Still needed: The complete visible-color order and explicit plane-wave/wavefront model are not taught in the inspected sections. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Predict frequency shifts from source–observer motion and compare their size; numerical Doppler formulas are outside this AP2 objective.

Essential knowledge checked: 14.5.A.1, 14.5.A.2

Study this section → The actual wave template explains approach/recession and relative motion; the formulas and speed calculations on the shared page are enrichment.

Still needed: The equal-source-and-observer-velocity case is not explicitly treated, so the full relative-motion scope is not demonstrated. Numerical Doppler bank problems are not counted as whole-question AP2 practice. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Add displacements, follow overlapping pulses through each other, and use difference frequency for beats; graphs and algebra.

Essential knowledge checked: 14.6.A.1, 14.6.A.2, 14.6.A.3, 14.6.A.4, 14.6.A.5, 14.6.A.6

Study this section → The explanation supplies displacement addition and constructive/destructive conditions.

Study this section → The beat-frequency relationship and varying loudness are present.

Still needed: The inspected explanation does not explicitly follow pulses passing through one another unchanged or explain the alternating phase relationship that produces beats. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Relate nodes, antinodes, harmonics, wavelength and speed on strings and in open/closed pipes, including fixed/loose ends; algebra and diagrams.

Essential knowledge checked: 14.6.B.1, 14.6.B.2, 14.6.B.3

Study this section → The actual template explains nodes, antinodes and open/closed-pipe harmonic conditions.

Still needed: The inspected explanation treats fixed strings and air columns but does not develop the loose-string-end cases explicitly. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Relate wavelength, aperture shape/width, angle and screen minima; use small-angle screen geometry only below 10°.

Essential knowledge checked: 14.7.A.1, 14.7.A.2, 14.7.A.3, 14.7.A.4, 14.7.A.6, 14.7.A.5

Study this section → The opening-size comparison explains the onset of spreading.

Study this section → Slit minima, central-maximum width and a contrasting circular-aperture resolution formula are present.

Study this section → The worked screen example relates the first minimum to screen distance and obtains the central-band width.

Still needed: The circular-aperture resolution formula does not explain how changing aperture shape changes the diffraction-pattern shape. The lab displays a fixed normalized intensity curve alongside changing numerical widths, so it is not credited as a calibrated screen-position graph. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Explain path differences, orders, grating dispersion and the single-slit envelope of a double-slit pattern; screen-distance approximation below 10°.

Essential knowledge checked: 14.8.A.1, 14.8.A.2, 14.8.A.3, 14.8.A.4, 14.8.A.5

Study this section → The template teaches fringe spacing, phase paths and changed experimental parameters.

Study this section → Grating orders, dispersion and wavelength dependence are taught.

Still needed: The single-slit diffraction envelope superimposed on double-slit fringes is not taught; the interactive boundary explicitly says its bars do not model that envelope.

Practise this objective →

Required depth: Track transmission/reflection phases and optical path to explain films and coatings; numerical calculations use normal incidence only.

Essential knowledge checked: 14.9.A.1, 14.9.A.2, 14.9.A.3, 14.9.A.4, 14.9.A.5

Study this section → Optical path, the one-reflection phase-reversal case and a quarter-wave coating are discussed.

Study this section → The worked coating example explicitly compares the three refractive indices, identifies both reflected phase flips and explains off-design wavelengths.

Still needed: The lesson does not state explicitly that refraction introduces no boundary phase reversal, or complete the reflected/transmitted/absorbed energy account at each interface. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use photon energy/momentum and de Broglie relations, interpret quantization and model limits; algebra, with particle-speed approximations stated.

Essential knowledge checked: 15.1.A.1, 15.1.A.2, 15.1.A.3, 15.1.A.4, 15.1.A.5

Study this section → The photon explanation includes energy, momentum and classical-model failure.

Study this section → The wavelength/momentum relation and scale at which diffraction matters are explained.

Study this section → Allowed standing-wave orbits link bound states to discrete values.

Still needed: The selected teaching does not give the complete blackbody/classical-model motivation or a clear quantum-particle double-slit account; photon propagation in media also needs explicit linkage. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use nuclear bookkeeping and circular-orbit force balance with standing electron wavelengths; energy levels only, excluding orbital shapes and probability functions.

Essential knowledge checked: 15.2.A.1, 15.2.A.2, 15.2.A.3

Study this section → Nuclide notation and isotope bookkeeping are taught.

Study this section → Coulomb-bound circular orbits, energy levels and integer-wavelength circumference are explained.

Study this section → The rendered foundation reminder explains the small positive nucleus, surrounding electrons and concentration of almost all atomic mass in the nucleus. Open the nuclear-atom reminder; quark detail is enrichment.

Still needed: Ion charge and the role of electron arrangements in interactions are not established explicitly in the selected teaching. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Read one-electron energy diagrams, match absorbed/emitted photons and identify spectra and ionization energy; algebraic energy differences.

Essential knowledge checked: 15.3.A.1, 15.3.A.2, 15.3.A.3, 15.3.A.4, 15.3.A.5

Study this section → The lesson connects discrete levels, both spectrum types, photon gaps and the ionization threshold.

Study this section → The model explains the electron–nucleus interaction and negative bound-state energy.

Still needed: No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Explain blackbody absorption/emission, continuous spectra, quantum necessity and temperature-dependent peak/power; use Wien and Stefan–Boltzmann algebraically.

Essential knowledge checked: 15.4.A.1, 15.4.A.2, 15.4.A.3

Study this section → Radiative balance, perfect-emitter limit, fourth-power radiation and peak-wavelength equations are present.

Still needed: The selected lesson does not teach the continuous intensity-per-wavelength spectrum or why classical physics fails and quantized Planck energy is needed. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use threshold/work function, photon-energy balance and stopping-potential measurements; work-function values are supplied, not memorized.

Essential knowledge checked: 15.5.A.1, 15.5.A.2, 15.5.A.3

Study this section → The frequency/intensity distinction, stopping potential and classical prediction comparison are explicitly taught.

Practise this objective →

Required depth: Use photon wavelength shift and conservation of energy/momentum including quantitative two-dimensional collisions; algebra, trigonometry and vectors.

Essential knowledge checked: 15.6.A.1, 15.6.A.2, 15.6.A.3

Study this section → The Compton paragraph and wavelength-shift relation explain the photon/electron exchange.

Still needed: The route states conservation and the final shift equation but does not work through quantitative two-dimensional photon/electron momentum components and recoil energy. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Apply nucleon, energy and momentum conservation, mass–energy conversion and strong-force reasoning to fission/fusion and spontaneous/induced processes; algebra.

Essential knowledge checked: 15.7.A.1, 15.7.A.2, 15.7.A.3, 15.7.A.4, 15.7.A.5, 15.7.A.6, 15.7.A.7, 15.7.A.8

Study this section → Binding energy, strong-force range, mass defect and induced fission/fusion are explained.

Still needed: Spontaneous fission and quantitative reaction-product momentum/energy constraints are not fully treated in the inspected lesson. No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use random-decay probability, half-life, decay constant and exponential survival/dating; logarithms allowed, no differential-equation derivation required.

Essential knowledge checked: 15.7.B.1, 15.7.B.2, 15.7.B.3

Study this section → Gamma decay is explicitly de-excitation of the same nucleus with unchanged A/Z, matching the Fall2026 clarification.

Study this section → Sample halving, wide half-life range and dating are explained.

Study this section → The exponential-decay and half-life/decay-constant relations are usable algebraically; the calculus derivation is enrichment.

Still needed: No canonical AP bank exercise has been independently verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Track alpha, beta± and gamma with nucleon/lepton/charge conservation; no memorized isotope routes, electron capture, neutron emission or weak-force mechanism.

Essential knowledge checked: 15.8.A.1, 15.8.A.2, 15.8.A.3

Study this section → The explanation distinguishes alpha, both beta signs and same-nucleus gamma emission.

Study this section → The rendered notes give neutral neutrinos/antineutrinos and opposite electron/positron charges with equal rest masses. Quark composition and lepton generations are enrichment.

Study this section → Both beta channels identify the emitted electron/antineutrino or positron/neutrino pair. The quark-level mechanism is enrichment for AP2.

Study this section → The second worked example accounts for the beta-minus electron and antineutrino lepton numbers, and connects the shared energy/momentum to a variable electron energy.

Still needed: The matched notes do not complete the required negligible-mass and weak/gravitational interaction explanation for neutrinos/antineutrinos, or explicitly apply nucleon, lepton and charge conservation together across every decay channel.

Practise this objective →

Required depth: Use charge signs, quantisation, point-charge modelling and Coulomb vectors. Quantitative force combinations involve at most four interacting charges unless symmetry simplifies more; recognise the electric origin of contact forces.

Essential knowledge checked: 8.1.A.1, 8.1.A.2, 8.1.A.3, 8.1.A.4

Study this section → Charge signs, electron transfer and quantisation.

Study this section → Point-charge inverse-square force, signs and units.

Study this section → Vector-force sums and equilibrium; use the AP four-charge boundary.

Still needed: The mapped lessons do not explicitly connect normal force, friction and tension to microscopic electric interactions (8.1.A.4). No matching canonical AP question was verified.

No practice question has yet been verified for this objective.

Required depth: Compare attraction/repulsion, relative microscopic strengths and why neutral bulk systems allow gravity to dominate on large scales.

Essential knowledge checked: 8.1.B.1, 8.1.B.2, 8.1.B.3

Study this section → The challenging example compares electric and gravitational proton–electron forces.

Still needed: The atomic force ratio is taught, but large-scale electrical neutrality and gravitational dominance need an explicit explanation. No matching canonical AP question was verified.

No practice question has yet been verified for this objective.

Required depth: Relate vacuum and material permittivity to polarisation and charge mobility. Use the qualitative conductor/insulator distinction and ε/ε₀; tensor susceptibility and molecular thermal models are extension.

Essential knowledge checked: 8.1.C.1, 8.1.C.2, 8.1.C.3, 8.1.C.4

Study this section → Mobile versus bound charge and qualitative polarisation.

Study this section → Use the dielectric-constant card and the bound-charge explanation. Susceptibility tensors, microscopic polarizability and thermal alignment calculations are outside this AP match.

Still needed: Lesson scope is mapped; no corresponding canonical AP bank question was verified in this audit.

No practice question has yet been verified for this objective.

Required depth: Track electron transfer in friction, contact and grounding; distinguish induced charge separation from a change in net charge.

Essential knowledge checked: 8.2.A.1, 8.2.A.2, 8.2.A.3

Study this section → Charge ledger and conservation.

Study this section → Friction, contact and the correct grounding sequence for induction.

Still needed: Lesson scope is mapped; no corresponding canonical AP bank question was verified in this audit.

No practice question has yet been verified for this objective.

Required depth: Use E=F/q for a non-disturbing probe; combine fields as vectors and interpret vector maps and field-line direction/density.

Essential knowledge checked: 8.3.A.1, 8.3.A.2, 8.3.A.3

Study this section → Source/probe distinction, signed force and vector field.

Study this section → Field-line arrows and density.

Study this section → Vector addition and null points.

Still needed: Lesson scope is mapped; no corresponding canonical AP bank question was verified in this audit.

No practice question has yet been verified for this objective.

Required depth: Distinguish zero field inside equilibrium conducting material from possibly nonzero fields inside charged insulators; include normal surface field and the exterior spherical result.

Essential knowledge checked: 8.3.B.1, 8.3.B.2

Study this section → Equilibrium surface charge, perpendicular external field and shielding limits.

Study this section → Use the inside/outside uniformly charged insulating sphere example; its charge is distributed through the volume, unlike the conductor.

Still needed: No outstanding teaching gap identified within the stated AP scope; the linked questions sample the objective rather than prove mastery.

Practise this objective →

Required depth: Integrate Coulomb contributions with symmetry for infinite line/cylinder, ring axis, arc centre, and finite line on-axis or on its perpendicular bisector. General arbitrary geometries are not required.

Essential knowledge checked: 8.4.A.1, 8.4.A.2

Study this section → Ring-axis integration and finite-line bisector geometry.

Study this section → Finite uniform rod on its axis: dq=λdx and the force integral.

Still needed: Arc-centre integration and a calculus derivation for an infinite line/cylinder are not demonstrated in the mapped lessons. The Gauss shortcut alone does not complete 8.4.

Practise this objective →

Required depth: Use the area normal, signed E·A, and the surface integral of E·dA. Distinguish an open-area flux from the net outward flux through a closed surface.

Essential knowledge checked: 8.5.A.1, 8.5.A.2, 8.5.A.3

Study this section → Uniform-field flux, normal-angle convention and outward sign.

Study this section → Integral flux and the conditions for factoring E out; the surface pieces explain positive, negative and zero contributions.

Still needed: Uniform-area and general closed-surface flux are taught; an explicit open-surface integral for nonuniform electric field is not developed.

Practise this objective →

Required depth: Use closed-surface flux and integrate charge density over the appropriate length, area or volume. Quantitative cases are restricted to point, spherical, cylindrical and planar symmetry; recognise Gauss law in Maxwell’s system.

Essential knowledge checked: 8.6.A.1, 8.6.A.2, 8.6.A.3, 8.6.A.4, 8.6.A.5, 8.6.A.6

Study this section → Sphere, line and sheet symmetry; no general density integration is taught here.

Study this section → Adds integral form, total versus enclosed sources, and the interior/exterior insulating sphere model.

Still needed: Mapped teaching states the density integral but does not work a variable-density example or situate electric Gauss law within the full Maxwell set. The reviewed sphere question supplies practice for the density step.

Practise this objective →

Required depth: Choose zero at infinite separation, retain charge signs, and sum each distinct pair once when assembling a multicharge system.

Essential knowledge checked: 9.1.A.1, 9.1.A.2, 9.1.A.3

Study this section → Two-charge potential energy and external versus field work.

Study this section → Scalar potential and the energy of an added test charge support the pairwise idea.

Still needed: An explicit total-energy calculation for several charges, with each pair counted once, is missing from these lesson sections. No matching canonical AP question was verified.

No practice question has yet been verified for this objective.

Required depth: Use signed scalar superposition and potential integrals. Calculus geometries: infinite line/cylinder, ring axis, arc centre, finite line on-axis or on the perpendicular bisector; include battery potential differences.

Essential knowledge checked: 9.2.A.1, 9.2.A.2, 9.2.A.3, 9.2.A.4

Study this section → Potential and potential difference as energy per charge.

Study this section → Signed scalar sums for point charges.

Study this section → Ring-axis potential integral and the point-charge reference.

Study this section → Source emf and terminal potential difference.

Still needed: The mapped lessons do not derive potential for finite lines, arcs and infinite lines/cylinders with an appropriate finite reference. Ring coverage must not stand for every permitted geometry.

Practise this objective →

Required depth: Differentiate a potential component, integrate E·dl for potential differences, and translate between equipotential maps and perpendicular electric-field vectors.

Essential knowledge checked: 9.2.B.1, 9.2.B.2, 9.2.B.3

Study this section → Gradient direction, orthogonality and work along equipotentials.

Study this section → Integrating radial fields and differentiating point/ring potentials.

Still needed: No outstanding teaching gap identified within the stated AP scope; the linked questions sample the objective rather than prove mastery.

Practise this objective →

Required depth: Use ΔU=qΔV and conservation of mechanical/electric energy, with the sign of the moving charge and any external work identified.

Essential knowledge checked: 9.3.A.1, 9.3.A.2

Study this section → Field work is the negative change in potential energy.

Study this section → Signed qΔV and positive/negative charge motion.

Study this section → Escape-energy example links the field integral to kinetic energy.

Still needed: No outstanding teaching gap identified within the stated AP scope; the linked questions sample the objective rather than prove mastery.

Practise this objective →

Required depth: Use fast charge redistribution, equipotential conductors, zero interior field, normal surface field, enhanced charge density at sharp curvature and external-field shielding.

Essential knowledge checked: 10.1.A.1, 10.1.A.2, 10.1.A.3, 10.1.A.4, 10.1.A.5, 10.1.A.6, 10.1.A.7

Study this section → Free carriers and excess surface charge.

Study this section → Equilibrium, curvature, normal field and empty-cavity shielding.

Study this section → Use the equilibrium/equipotential and grounding explanations; Laplace-equation proofs and detailed cavity boundary-value work are extension.

Still needed: No outstanding teaching gap identified within the stated AP scope; the linked questions sample the objective rather than prove mastery.

Practise this objective →

Required depth: Connected conductors reach equal potential, not generally equal charge. Treat Earth as the zero-potential reservoir and explain grounded induction.

Essential knowledge checked: 10.2.A.1, 10.2.A.2, 10.2.A.3

Study this section → Contact equalises potential and induction needs the correct grounding sequence.

Study this section → Use the joined-sphere and grounding explanations; detailed cavity-image problems are extension.

Still needed: Lesson scope is mapped; no corresponding canonical AP bank question was verified in this audit.

No practice question has yet been verified for this objective.

Required depth: Relate geometry/material to capacitance, plate fields and projectile-like charged-particle motion, and stored energy to charging work. Quantitative capacitor shapes are parallel plates, concentric spheres and coaxial cylinders.

Essential knowledge checked: 10.3.A.1, 10.3.A.2, 10.3.A.3, 10.3.A.4, 10.3.A.5

Study this section → Parallel plates, Q/V, geometry and all stored-energy forms.

Study this section → Uniform force and particle acceleration between plates.

Study this section → Use Gauss-law/radial-integral derivations for coaxial and concentric spherical capacitors; cable impedance and breakdown optimisation are extension.

Study this section → Use the work-of-charging derivation and equivalent energy forms; energy-density machinery and plate-pressure calculations are extension.

Still needed: No outstanding teaching gap identified within the stated AP scope; the linked questions sample the objective rather than prove mastery.

Practise this objective →

Required depth: Explain bound-charge polarisation, opposing internal field, κ=ε/ε₀ and C=κC₀. Identify fixed charge versus fixed voltage before predicting field, voltage and energy.

Essential knowledge checked: 10.4.A.1, 10.4.A.2, 10.4.A.3, 10.4.A.4, 10.4.A.5

Study this section → Qualitative bound-charge polarisation.

Study this section → Use the first three explanation cards and fixed-charge/fixed-voltage formula cards. Partial insertion and dielectric-force derivations are extension.

Study this section → Use bound-charge separation and opposing field; molecular susceptibility and tensor calculations are extension.

Still needed: No outstanding teaching gap identified within the stated AP scope; the linked questions sample the objective rather than prove mastery.

Practise this objective →

Required depth: Use I=dq/dt, conventional-current direction and carrier drift. Distinguish scalar current from vector J, integrate J over a cross-section and use E=ρJ.

Essential knowledge checked: 11.1.A.1, 11.1.A.2, 11.1.A.3, 11.1.A.4

Study this section → Drift superposed on random motion and conventional-current direction.

Study this section → Instantaneous current and integrated charge.

Study this section → Use current-density, flux-of-J and local Ohm-law sections including the nonuniform J(r) integral. Mobility, quantum transport and skin-depth calculations are extension.

Still needed: No outstanding teaching gap identified within the stated AP scope; the linked questions sample the objective rather than prove mastery.

Practise this objective →

Required depth: Recognise open, closed and short circuits; identify shared elements in multiple loops and standard symbols, including capacitors and inductors. Diagrams use conventional current unless stated otherwise.

Essential knowledge checked: 11.2.A.1, 11.2.A.2, 11.2.A.3, 11.2.A.4

Study this section → Closed paths, source/switch symbols and meter wiring.

Study this section → Shared branches and independent loop equations.

Still needed: The mapped symbols lesson does not provide the full AP capacitor/inductor symbol set and explicit short-circuit topology instruction. No canonical AP question was verified for the whole objective.

No practice question has yet been verified for this objective.

Required depth: Use R=ρL/A for a uniform specimen, material and temperature dependence, and integrate dR=ρ(x)dx/A when resistivity varies along its length.

Essential knowledge checked: 11.3.A.1, 11.3.A.2

Study this section → Uniform-wire geometry, material resistivity and temperature.

Still needed: The required variable-resistivity integral is not demonstrated. No corresponding canonical AP bank question was verified.

No practice question has yet been verified for this objective.

Required depth: Read resistance from a linear I–V slope, distinguish an ideal constant-resistance element from temperature-dependent real components, and account for electrical energy becoming heat.

Essential knowledge checked: 11.3.B.1

Study this section → Ohm-law definition, slope, and constant-temperature physical conditions.

Study this section → Filament heating changes resistance; it is not an ideal ohmic element.

Still needed: The CED ideal-ohmic resistivity convention needs to be stated explicitly alongside the real-material temperature caveat. No matching canonical AP question was verified.

No practice question has yet been verified for this objective.

Required depth: Use P=IV and resistive forms, compare bulb brightness by power and keep the assessed energy account to mechanical/electrical transfer with thermal dissipation acknowledged.

Essential knowledge checked: 11.4.A.1, 11.4.A.2

Study this section → Power derivation, resistive heating and lamp ratings.

Still needed: Power and heating are taught; the mapped lesson does not explicitly teach relative bulb brightness in changing circuit arrangements.

Practise this objective →

Required depth: Reduce series/parallel combinations using common series current and parallel voltage, and explain why extra parallel paths lower equivalent resistance.

Essential knowledge checked: 11.5.A.1, 11.5.A.2

Study this section → Series, parallel and mixed-network examples with current/voltage accounting.

Still needed: Lesson scope is mapped; no corresponding canonical AP bank question was verified in this audit.

No practice question has yet been verified for this objective.

Required depth: Model source internal resistance in series, emf as open-circuit voltage, and terminal voltage under load. Neglect wire resistance only when justified relative to other elements; unequal ideal batteries in parallel are outside assessment.

Essential knowledge checked: 11.5.B.1, 11.5.B.2, 11.5.B.3

Study this section → Emf, lost volts and load dependence.

Study this section → Calculate wire resistance when it cannot be neglected.

Study this section → Connecting wires are explicitly idealised in the schematic model.

Still needed: Lesson scope is mapped; no corresponding canonical AP bank question was verified in this audit.

No practice question has yet been verified for this objective.

Required depth: Connect ammeters in series and voltmeters in parallel. Ideal limits are zero and infinite resistance respectively; finite meter resistance changes the measured circuit.

Essential knowledge checked: 11.5.C.1, 11.5.C.2, 11.5.C.3

Study this section → Meter connections, ideal resistances and consequences of incorrect wiring.

Study this section → Worked finite-resistance voltmeter example shows loading.

Still needed: No outstanding teaching gap identified within the stated AP scope; the linked questions sample the objective rather than prove mastery.

Practise this objective →

Required depth: Apply signed potential changes around each closed loop as conservation of energy and represent potential against position in that loop.

Essential knowledge checked: 11.6.A.1, 11.6.A.2

Study this section → Energy conservation and signed loop equations.

Study this section → Energy-per-charge account across a source and components.

Still needed: The mapped teaching lacks a worked potential-versus-position graph around a loop (11.6.A.2.ii).

Practise this objective →

Required depth: Use current balance at a junction as the conservation of charge; choose directions and interpret a negative result.

Essential knowledge checked: 11.7.A.1, 11.7.A.2

Study this section → Junction-current bookkeeping and solved branch-current examples.

Still needed: Lesson scope is mapped; no corresponding canonical AP bank question was verified in this audit.

No practice question has yet been verified for this objective.

Required depth: Use equal charge in series, equal voltage in parallel, reciprocal series capacitance and additive parallel capacitance; check the series result is below every component.

Essential knowledge checked: 11.8.A.1, 11.8.A.2

Study this section → Charge-conservation derivation for both capacitor arrangements, with a series numerical example.

Still needed: Lesson scope is mapped; no corresponding canonical AP bank question was verified in this audit.

No practice question has yet been verified for this objective.

Required depth: Write the loop differential equation and connect its charging/discharge solutions to q, I, V and energy; use τ=RC, initial limits, 63% growth, 37% remaining and long-time steady states.

Essential knowledge checked: 11.8.B.1, 11.8.B.2, 11.8.B.3

Study this section → Discharge ODE, exponential decay and time constant; this lesson alone does not teach charging.

Study this section → Adds charging loop/power balance, charging functions, initial short-circuit behaviour and asymptotic energy; use the RC subset.

Still needed: The mapped lesson set displays charging functions and loop/power balance, but not a step-by-step charging ODE solution or mixed-branch switching analysis. The reviewed charging question supplies the derivation practice.

Practise this objective →

Required depth: Interpret magnetic vector maps, dipoles and closed field lines; connect the absence of monopoles to integral Gauss law for magnetism and its place in Maxwell’s equations.

Essential knowledge checked: 12.1.A.1, 12.1.A.2, 12.1.A.3

Study this section → Dipoles, field maps and closed line direction.

Study this section → Use the integral-law card and first three explanation cards. Divergence, vector potentials, boundary-value proofs and monopole searches are extension.

Still needed: Lesson scope is mapped; no corresponding canonical AP bank question was verified in this audit.

No practice question has yet been verified for this objective.

Required depth: Relate microscopic charge motion/dipoles to permanent and induced magnetisation, compass alignment, Earth’s dipole field, and ferro-, para- and diamagnetic response.

Essential knowledge checked: 12.1.B.1, 12.1.B.2, 12.1.B.3, 12.1.B.4

Study this section → Ferromagnetic domains, induced/permanent magnetism and compass alignment.

Still needed: Paramagnetism and diamagnetism, plus their contrasting microscopic response, are not taught in the mapped lesson. No corresponding canonical AP question was verified.

No practice question has yet been verified for this objective.

Required depth: Interpret permeability as magnetic material response, distinguish μ from μ₀, and recognise that material permeability depends on temperature, orientation and applied field.

Essential knowledge checked: 12.1.C.1, 12.1.C.2, 12.1.C.3

Study this section → Vacuum permeability and an iron-core relative-permeability example.

Still needed: A numerical core multiplier does not teach the full qualitative definition or nonconstant temperature/orientation/field dependence. No corresponding canonical AP question was verified.

No practice question has yet been verified for this objective.

Required depth: Predict how a moving point charge produces B: dependence on velocity and source–point distance, perpendicular direction from the right-hand rule, and maximum field for transverse geometry.

Essential knowledge checked: 12.2.A.1

Still needed: No AP-visible lesson section or canonical AP question was verified for the magnetic field made by a single moving charge. A force on a charge and a wire’s magnetic field are different objectives.

No practice question has yet been verified for this objective.

Required depth: Use the magnetic cross-product direction and magnitude, combine independent electric/magnetic forces and explain Hall voltage from charge separation. Keep motion nonrelativistic.

Essential knowledge checked: 12.2.B.1, 12.2.B.2, 12.2.B.3

Study this section → Angle-dependent magnetic force, reversed direction for negative charge, circular/helical motion and crossed-field selector.

Study this section → Hall-effect balance and combined electric/magnetic forces.

Still needed: No outstanding teaching gap identified within the stated AP scope; the linked questions sample the objective rather than prove mastery.

Practise this objective →

Required depth: Integrate current elements with direction and superposition. Quantitative geometries include a straight-wire perpendicular bisector, a circular-loop axis and the centre of a circular arc.

Essential knowledge checked: 12.3.A.1, 12.3.A.2, 12.3.A.3

Study this section → Biot–Savart current element and full-loop centre derivation.

Study this section → Wire/coil direction and standard field values.

Still needed: The mapped lesson does not derive off-centre loop-axis fields, finite straight-wire fields or arc-centre fields. A loop-centre example cannot certify every permitted geometry. No corresponding canonical AP bank question was verified.

No practice question has yet been verified for this objective.

Required depth: Integrate the directed element I dl×B where required, and use the angle-dependent straight-wire reduction when the field is uniform.

Essential knowledge checked: 12.3.B.1

Study this section → Uniform straight-wire force and direction.

Study this section → Integrates force along a rod in a varying transverse field.

Still needed: The scalar varying-field integral is taught, but an explicit vector line-integral treatment for changing wire direction is missing.

Practise this objective →

Required depth: Choose symmetric Amperian paths for long wires/solenoids and conducting slabs/cylinders, including enclosed-current density. Add fields by superposition. Changing E generates B conceptually; quantitative displacement-current use is not required.

Essential knowledge checked: 12.4.A.1, 12.4.A.2, 12.4.A.3, 12.4.A.4

Study this section → Wire and solenoid symmetry with a circulation sum; Hall-effect content is a separate objective.

Study this section → Integrates current density over the cross-section; use this to prepare the enclosed-current calculation.

Still needed: Missing lesson depth includes the circulation integral, slab and solid-cylinder derivations, and the qualitative changing-electric-field term in Maxwell’s fourth equation. Worked bank solutions support only the named cases.

Practise this objective →

Required depth: Use signed B·A for a uniform field and integrate B·dA over a general surface; choose an outward normal for closed surfaces.

Essential knowledge checked: 13.1.A.1, 13.1.A.2

Study this section → Uniform flux, area-normal angle and flux linkage.

Study this section → Closed-surface integral and outward/inward signs. The divergence/vector-potential material is extension.

Still needed: General open-surface flux integration for a nonuniform magnetic field is not developed in the mapped teaching.

Practise this objective →

Required depth: Differentiate flux from changing field, area or orientation; include N turns and Lenz direction. Recognise induced electric-field circulation and electromagnetic-wave speed c=1/√(μ₀ε₀); a Maxwell wave-speed derivation is not assessed.

Essential knowledge checked: 13.2.A.1, 13.2.A.2, 13.2.A.3, 13.2.A.4

Study this section → Changing-flux mechanisms and induced emf.

Study this section → Direction from opposition to the flux change.

Study this section → Time-dependent flux and motional-emf derivatives.

Study this section → Use only the first explanation for Faraday law as electric-field circulation; bulk loss, lamination and magnetic Reynolds-number calculations are extension.

Still needed: The mapped set still lacks the explicit Maxwell field-coupling/wave-speed connection. The changing-field/area induction subset is supported.

Practise this objective →

Required depth: Combine induced current, magnetic force and Newton’s law for a conducting loop; only portions in the external field feel that force. Include possible translation/rotation and resistance/velocity dependence.

Essential knowledge checked: 13.3.A.1, 13.3.A.2, 13.3.A.3, 13.3.A.4

Study this section → Induced opposition and mechanical-to-thermal energy transfer.

Study this section → Magnetic force on the current-carrying segment.

Study this section → Use the drag/damping and energy-account explanations. Detailed bulk-current loss formulae, skin effects and levitation are extension.

Still needed: Explicit lesson treatment of a moving wire loop partially entering/leaving a field and rotational acceleration remains incomplete. Reviewed questions provide the sliding-rod translation subset.

Practise this objective →

Required depth: Relate inductance to conductor geometry and solenoid μN²A/length; use induced emf −L dI/dt and stored energy ½LI² with conservation during transfer.

Essential knowledge checked: 13.4.A.1, 13.4.A.2, 13.4.A.3

Study this section → Self-induced emf, magnetic energy and release on current change.

Still needed: The solenoid inductance dependence/formula and its derivation from geometry are not taught in the mapped school lesson.

Practise this objective →

Required depth: Apply the loop differential equation to resistor–single-inductor circuits; describe growth/decay, τ=L/R, initial tangent and 63%/37% values, energy loss and the long-time wire limit.

Essential knowledge checked: 13.5.A.1, 13.5.A.2, 13.5.A.3, 13.5.A.4

Study this section → Growth/decay functions, time constant, initial tangent and steady-state wire behaviour.

Still needed: The lesson shows the exponential solutions but does not explicitly construct and solve the LR loop differential equation. The mapped bank family supplies that derivation practice.

Practise this objective →

Required depth: For an ideal capacitor–single-inductor loop, conserve electric plus magnetic energy to find maximum current, derive d²q/dt²=−q/(LC) and ω=1/√(LC). Damped/driven RLC, impedance resonance and quality factor are extension.

Essential knowledge checked: 13.6.A.1, 13.6.A.2, 13.6.A.3

Study this section → AP subset: the first two formula cards and first explanation, “The ideal loop is a harmonic oscillator”; use the Easy maximum-current example. The rest of this shared lesson develops RLC damping, driven resonance, phase and Q beyond this objective.

Still needed: Ideal LC teaching is mapped explicitly; no corresponding canonical AP bank question was verified. The lesson’s Easy worked example is support, not an exam-bank question.

No practice question has yet been verified for this objective.

Required depth: Use components and explicit unit-vector notation, including directional basis vectors, before calculus.

Essential knowledge checked: 1.1.A.1, 1.1.A.2, 1.1.A.3, 1.1.A.4, 1.1.A.5

Study this section → The visible comparison distinguishes magnitude-only quantities from directed quantities; the adjacent scale drawing shows vector magnitude.

Study this section → The component panel resolves a vector with trigonometry and preserves the chosen axes.

Study this section → Same-direction and opposite-direction addition are explicit; the component laboratory also handles angled vectors.

Study this section → The component and unit-basis rules, normalized direction vector, dot product and torque cross product are taught. The torque paragraph explicitly applies the right-hand rule; other vector-product applications are optional.

Study this section → The fixed-basis paragraphs differentiate and integrate each coordinate with initial conditions; the reduction paragraph sets the perpendicular coordinate to zero for a plane. Use two components for quantitative C Mechanics. Helices and three-dimensional geometric tests are optional.

Still needed: Component unit vectors and normalization are taught; add explicit radial-position unit-vector notation to complete the required convention. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use a signed one-axis coordinate and compare endpoints; explicitly justify replacing an extended object by a point.

Essential knowledge checked: 1.2.A.1, 1.2.A.2

Study this section → The origin, signed coordinate and displacement model are explicit; a particle-model validity discussion is not established here.

Still needed: Add a short decision example for when size and internal motion may be ignored. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Compare average rates with instantaneous velocity and acceleration, including a change of direction.

Essential knowledge checked: 1.2.B.1, 1.2.B.2, 1.2.B.3, 1.2.B.4, 1.2.B.5

Study this section → The rate panel compares speed and signed velocity using distance and displacement.

Study this section → The interactive explains acceleration signs by comparison with velocity, rather than equating negative acceleration with slowing.

Study this section → The shrinking-time-interval laboratory provides the average-to-instantaneous bridge; AP1 uses its visual interpretation only.

Study this section → The velocity and acceleration directions are shown together with the radial acceleration magnitude.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Differentiate and integrate motion functions with explicit initial conditions and consistent units.

Essential knowledge checked: 1.2.C.1, 1.2.C.2

Study this section → The derivative chain connects position, velocity and acceleration using functions and graphs.

Study this section → The integration laboratory accumulates signed velocity area and adds the initial position.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Join motion functions, slopes, areas and constant-acceleration special cases using calculus where acceleration varies.

Essential knowledge checked: 1.3.A.1, 1.3.A.2, 1.3.A.3, 1.3.A.4

Study this section → Velocity-time slope and signed area are taught together with a changing-motion display.

Study this section → The equation panel restricts the algebraic kinematics equations to constant acceleration.

Study this section → The free-fall section treats constant downward acceleration and the difference between zero velocity and zero acceleration.

Study this section → The derivative chain connects position, velocity and acceleration using functions and graphs.

Study this section → The integration laboratory accumulates signed velocity area and adds the initial position.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Name inertial observers and compare their motion descriptions before transforming coordinates.

Essential knowledge checked: 1.4.A.1

Study this section → Observer labels, relative velocities and equal accelerations in constant-relative-velocity frames are explicit. The boat example also contains optional two-dimensional material.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Transform relative velocities between ordinary inertial frames and compare their accelerations; no relativistic model is needed.

Essential knowledge checked: 1.4.B.1, 1.4.B.2

Study this section → Observer labels, relative velocities and equal accelerations in constant-relative-velocity frames are explicit. The boat example also contains optional two-dimensional material.

Study this section → Same-direction and opposite-direction addition are explicit; the component laboratory also handles angled vectors.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Quantitative C Mechanics calculations are planar; use component functions for nonuniform acceleration. The cross-course three-dimensional extension is not a required calculation here.

Essential knowledge checked: 1.5.A.1, 1.5.A.2, 1.5.A.3, 1.5.A.4

Study this section → The lesson separates perpendicular motions and reconnects them with a shared time; projectile graphs and horizontal launches follow.

Study this section → The component panel resolves a vector with trigonometry and preserves the chosen axes.

Study this section → The derivative chain connects position, velocity and acceleration using functions and graphs.

Study this section → The integration laboratory accumulates signed velocity area and adds the initial position.

Study this section → The fixed-basis paragraphs differentiate and integrate each coordinate with initial conditions; the reduction paragraph sets the perpendicular coordinate to zero for a plane. Use two components for quantitative C Mechanics. Helices and three-dimensional geometric tests are optional.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: A system choice must explain which interactions are internal and which transfers cross the boundary.

Essential knowledge checked: 2.1.A.1, 2.1.A.2, 2.1.A.3, 2.1.A.4, 2.1.A.5, 2.1.A.6

Study this section → The diagram rules isolate a system, identify external interactions and choose axes; they do not spell out all College Board drawing conventions.

Study this section → System boundaries, external transfers and conversion into internal energy are explained.

Still needed: Add explicit examples where external interactions alter internal structure, and distinguish a system’s properties from the properties of its parts. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use weighted coordinates and continuous mass integrals, with the appropriate linear, surface or volume density element.

Essential knowledge checked: 2.1.B.1, 2.1.B.2, 2.1.B.3, 2.1.B.4

Study this section → The lesson gives weighted coordinates, the continuous first moment, symmetry, and a composite lamina example.

Study this section → The loading integral and first moment demonstrate a one-dimensional continuous-weight analogue of the mass integral.

Study this section → The pressure-difference derivation of buoyancy is explicit for a prism, with the surface integral identified for other shapes.

Still needed: The integral and a line-load analogue are present; explicit surface-density and nonuniform-volume centre-of-mass constructions are missing. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Identify the interaction partner and whether contact is involved before assigning a force.

Essential knowledge checked: 2.2.A.1, 2.2.A.2

Study this section → The diagram rules isolate a system, identify external interactions and choose axes; they do not spell out all College Board drawing conventions.

Study this section → The interaction-pair examples put each force on a different body.

Study this section → The force library distinguishes weight, applied force and normal contact force.

Still needed: Add the microscopic electric origin of contact forces and an explicit explanation that an object cannot provide its own net external force. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Select axes and draw the actual forces on a dot model; force components belong in the calculation rather than as extra forces.

Essential knowledge checked: 2.2.B.1, 2.2.B.2, 2.2.B.3, 2.2.B.4

Study this section → The diagram rules isolate a system, identify external interactions and choose axes; they do not spell out all College Board drawing conventions.

Study this section → The board adds signed force components independently and connects the resultant to acceleration.

Still needed: Add explicit dot-origin and side-by-side same-direction arrow conventions; the current lesson does not establish every required drawing rule. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Follow equal-and-opposite forces through a cord/system model; use ideal cords and pulleys, with qualitative attention to massive cords.

Essential knowledge checked: 2.3.A.1, 2.3.A.2, 2.3.A.3

Study this section → The interaction-pair examples put each force on a different body.

Study this section → The visible model states equal tension for a massless cord and ideal pulley, and notes that real massive cords can differ.

Study this section → The lesson defines a system/time interval and compares external impulse with cancelling internal impulses.

Still needed: Explain tension through neighbouring cord segments and work through the varying-tension massive-cord case; make the ideal pulley assumptions explicit. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Distinguish zero acceleration from zero speed and balance each direction independently in an inertial frame.

Essential knowledge checked: 2.4.A.1, 2.4.A.2, 2.4.A.3, 2.4.A.4, 2.4.A.5

Study this section → The law selector states constant-velocity equilibrium, proportional acceleration, and equal-and-opposite interaction pairs.

Study this section → The board adds signed force components independently and connects the resultant to acceleration.

Study this section → Observer labels, relative velocities and equal accelerations in constant-relative-velocity frames are explicit. The boat example also contains optional two-dimensional material.

Study this section → The first explanation defines an inertial frame through interaction-free motion and compares constant-velocity frames. The uniform-acceleration paragraph explains a mass-proportional effective gravity; rotating-frame and Coriolis calculations are optional.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Calculate the resultant vector and compare accelerations at different masses; extend the object model to a system’s centre of mass.

Essential knowledge checked: 2.5.A.1, 2.5.A.2, 2.5.A.3

Study this section → The second-law statement and force-acceleration display show the resultant direction and inverse mass dependence.

Study this section → The board adds signed force components independently and connects the resultant to acceleration.

Still needed: The centre-of-mass form for an extended system needs explicit teaching alongside the point-object examples. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Use centre-to-centre separation, distinguish force from field, and interpret field using a small test mass.

Essential knowledge checked: 2.6.A.1, 2.6.A.2, 2.6.A.3

Study this section → The inverse-square model uses centre-to-centre separation, exterior spherical masses, and equal-and-opposite attraction.

Study this section → The gravity applications connect local field strength, weight and orbital free fall; the explicit zero-total-energy argument gives escape speed.

Still needed: Add an explicit gravitational-field test-mass definition and a force-versus-field comparison. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Choose the approximately constant-field model only when height changes are small compared with planetary radius.

Essential knowledge checked: 2.6.B.1, 2.6.B.2

Study this section → The gravity applications connect local field strength, weight and orbital free fall; the explicit zero-total-energy argument gives escape speed.

Study this section → The near-surface and inverse-square energy models are distinguished, including the choice of zero.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Analyze support force separately from gravity; apparent weightlessness is a dynamical condition.

Essential knowledge checked: 2.6.C.1, 2.6.C.2, 2.6.C.3, 2.6.C.4

Study this section → The passenger example identifies the scale reading as normal force and explains free-fall apparent weightlessness.

Study this section → The first explanation defines an inertial frame through interaction-free motion and compares constant-velocity frames. The uniform-acceleration paragraph explains a mass-proportional effective gravity; rotating-frame and Coriolis calculations are optional.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Separate resistance to acceleration from gravitational coupling, then compare their measured equivalence.

Essential knowledge checked: 2.6.D.1, 2.6.D.2, 2.6.D.3

Study this section → The second-law statement and force-acceleration display show the resultant direction and inverse mass dependence.

Study this section → The inverse-square model uses centre-to-centre separation, exterior spherical masses, and equal-and-opposite attraction.

Still needed: The lessons use both meanings but do not explicitly distinguish and experimentally relate inertial and gravitational mass. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Apply the shell theorem to spherical shells and uniform solid spheres; a proof of the theorem is not required.

Essential knowledge checked: 2.6.E.1, 2.6.E.2, 2.6.E.3

Study this section → The inverse-square model uses centre-to-centre separation, exterior spherical masses, and equal-and-opposite attraction.

Still needed: The exterior point-mass approximation is taught, but the zero interior-shell field and enclosed-mass interior-sphere construction lack a lesson. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Use relative sliding to choose direction and the perpendicular normal force in the kinetic-friction law.

Essential knowledge checked: 2.7.A.1, 2.7.A.2

Study this section → Static friction adjusts up to a limit; the kinetic law and relative-sliding direction test are explicit.

Still needed: Add the model’s contact-area independence and a material-pair comparison. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Determine the required static force first, then test its maximum; do not automatically substitute the limiting value.

Essential knowledge checked: 2.7.B.1, 2.7.B.2, 2.7.B.3

Study this section → Static friction adjusts up to a limit; the kinetic law and relative-sliding direction test are explicit.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Compare an ideal linear negligible-mass spring with departures caused by spring mass or nonlinear force response.

Essential knowledge checked: 2.8.A.1, 2.8.A.2, 2.8.A.3

Study this section → Restoring force, signed deformation and the quadratic elastic store are explicitly linked.

Study this section → The extension model and elastic-range qualification teach the linear force law; restoring-force sign is clearer in the elastic-energy lesson.

Still needed: The elastic range is discussed, but the effect of nonnegligible spring mass is not taught. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Analyze pure series or pure parallel spring combinations; mixed networks are outside the specified scope.

Essential knowledge checked: 2.8.B.1

Still needed: No AP-visible lesson was verified for equivalent spring constants. Add force/displacement arguments for series and parallel assemblies. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Set up a resistive-force differential equation, separate variables with initial conditions, and connect its velocity solution to acceleration, displacement and terminal limits.

Essential knowledge checked: 2.9.A.1, 2.9.A.2, 2.9.A.3

Study this section → The model sets up velocity-dependent Newton equations, balances terminal forces and interprets the asymptotic exponential solution. It states the solution without deriving it by separation or integrating displacement; quadratic-drag fluid details are optional.

Still needed: Add the separation-of-variables derivation with initial conditions and integrate the velocity to obtain displacement. The authored lesson states and interprets the velocity solution; the bank provides worked derivation practice. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Resolve radial and tangential accelerations, including nonuniform circular motion; analyze real-force diagrams for conical, vertical-circle and banked-turn cases.

Essential knowledge checked: 2.10.A.1, 2.10.A.2, 2.10.A.3, 2.10.A.4, 2.10.A.5

Study this section → The velocity and acceleration directions are shown together with the radial acceleration magnitude.

Study this section → Real radial forces, friction-limited turning, ideal banking and vertical-circle force signs are taught.

Study this section → The lesson explains lever geometry, signed torque, fixed-axis angular acceleration and constant-angular-acceleration equations.

Still needed: Add conical-pendulum analysis, explicit minimum speed at a loop top, and the qualitative effect of friction on a banked turn. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Use circular-orbit gravity and radial acceleration; first/second Kepler-law work is not required for this objective.

Essential knowledge checked: 2.10.B.1

Study this section → The shared astronomy lesson includes circular orbital speed and Kepler scaling among broader astronomy content.

Study this section → The shared section derives the circular-orbit period relation and escape speed; its astronomy/error/black-hole extensions are outside these mechanics objectives.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Compute the scalar motion energy and compare square-speed changes in a named frame.

Essential knowledge checked: 3.1.A.1, 3.1.A.2, 3.1.A.3

Study this section → The scalar kinetic-energy formula and square-speed scaling are explained.

Study this section → Observer labels, relative velocities and equal accelerations in constant-relative-velocity frames are explicit. The boat example also contains optional two-dimensional material.

Still needed: Add an explicit calculation showing that observers assign different kinetic energies to the same object. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Use dot products and definite path integrals for variable-force work, while distinguishing mechanical energy transfer from internal dissipation.

Essential knowledge checked: 3.2.A.1, 3.2.A.2, 3.2.A.3, 3.2.A.4, 3.2.A.5

Study this section → The work model makes the system boundary, displacement and force direction explicit.

Study this section → The signed force-displacement area gives work for varying force.

Study this section → The net-work balance converts initial and final kinetic energies into a speed calculation.

Study this section → The calculus lesson treats variable-force work as a path integral and connects power with the energy rate.

Study this section → The lesson links conservative work, negative potential slope and the energy landscape.

Study this section → The model builds the dot-product path integral and compares conservative gravity with path-dependent friction. C Mechanics can use the calculus; AP Physics 1 uses only the constant-gravity and constant-friction path comparison, including a closed loop.

Still needed: The conservative closed-path comparison is taught. Add the distinction between displacement of the force application point and displacement of the centre of mass. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Obtain force from a potential derivative, classify equilibria, and combine the relevant interaction-energy models with a stated reference zero.

Essential knowledge checked: 3.3.A.1, 3.3.A.2, 3.3.A.3, 3.3.A.4, 3.3.A.5, 3.3.A.6, 3.3.A.7, 3.3.A.8

Study this section → The near-surface and inverse-square energy models are distinguished, including the choice of zero.

Study this section → Restoring force, signed deformation and the quadratic elastic store are explicitly linked.

Study this section → The lesson links conservative work, negative potential slope and the energy landscape.

Study this section → The energy-stability section interprets equilibrium through the potential-energy landscape and restoring tendency.

Still needed: Potential derivatives and stability are supported, but pairwise potential-energy addition for more than two objects and the system ownership of potential energy need explicit treatment. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: A useful energy account depends on which interacting objects lie inside the chosen boundary.

Essential knowledge checked: 3.4.A.1, 3.4.A.2

Study this section → System boundaries, external transfers and conversion into internal energy are explained.

Still needed: Add a direct single-particle-versus-interacting-system comparison; the broad energy-store list does not establish the mechanical system distinction. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Balance mechanical stores with external transfers and internal dissipation; thermal and sound conversion should be named where relevant.

Essential knowledge checked: 3.4.B.1, 3.4.B.2, 3.4.B.3, 3.4.B.4

Study this section → System boundaries, external transfers and conversion into internal energy are explained.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Revisit the same process with different boundaries before deciding whether mechanical energy is constant.

Essential knowledge checked: 3.4.C.1, 3.4.C.2, 3.4.C.3

Study this section → System boundaries, external transfers and conversion into internal energy are explained.

Study this section → The work model makes the system boundary, displacement and force direction explicit.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Connect average work/energy transfer with the instantaneous derivative and force-velocity dot product.

Essential knowledge checked: 3.5.A.1, 3.5.A.2, 3.5.A.3, 3.5.A.4, 3.5.A.5

Study this section → The formula panel compares average transfer rate with instantaneous force-velocity power.

Study this section → The calculus lesson treats variable-force work as a path integral and connects power with the energy rate.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use signed/vector momentum and identify whether a short collision or an explosion can be treated as an internal interaction.

Essential knowledge checked: 4.1.A.1, 4.1.A.2, 4.1.A.3

Study this section → Signed momentum and vector addition for a system are explicit.

Study this section → The lesson defines a system/time interval and compares external impulse with cancelling internal impulses.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Integrate net force over time and differentiate momentum; interpret both graph representations.

Essential knowledge checked: 4.2.A.1, 4.2.A.2, 4.2.A.3, 4.2.A.4, 4.2.A.5

Study this section → The average-force model, signed force-time area and rebound momentum change are taught.

Study this section → Force is read as momentum-time slope and integrated over time; the variable-mass wording needs the separate system-balance qualification.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Use the impulse-momentum theorem for fixed mass and the specified constant-velocity changing-mass case, with the system boundary made explicit.

Essential knowledge checked: 4.2.B.1, 4.2.B.2

Study this section → The average-force model, signed force-time area and rebound momentum change are taught.

Study this section → Force is read as momentum-time slope and integrated over time; the variable-mass wording needs the separate system-balance qualification.

Study this section → The extension distinguishes a fixed-particle momentum derivative from an open-system momentum balance; it is not a worked variable-mass calculation.

Still needed: Add a worked constant-velocity mass-change model with a correct open-system momentum balance. The shared momentum-calculus wording is overbroad about variable mass and cannot certify this demand. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Calculate one- and two-dimensional collisions using vector/component balances; keep three-dimensional collisions qualitative.

Essential knowledge checked: 4.3.A.1, 4.3.A.2, 4.3.A.3, 4.3.A.4

Study this section → The lesson defines a system/time interval and compares external impulse with cancelling internal impulses.

Study this section → The lesson compares elastic and inelastic collisions, centre-of-mass motion and energy conversion.

Study this section → The worked method conserves each perpendicular momentum component before recombining velocity.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: State the chosen system and external impulse before claiming constant momentum.

Essential knowledge checked: 4.3.B.1, 4.3.B.2, 4.3.B.3

Study this section → The lesson defines a system/time interval and compares external impulse with cancelling internal impulses.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Compare total kinetic energy, individual velocities and the sticking limit; momentum and kinetic-energy conservation are separate tests.

Essential knowledge checked: 4.4.A.1, 4.4.A.2, 4.4.A.3, 4.4.A.4, 4.4.A.5

Study this section → The lesson compares elastic and inelastic collisions, centre-of-mass motion and energy conversion.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

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Required depth: Differentiate/integrate angular functions and use constant-acceleration special cases; signed clockwise/counterclockwise descriptions suffice for kinematics.

Essential knowledge checked: 5.1.A.1, 5.1.A.2, 5.1.A.3, 5.1.A.4

Study this section → The lesson connects radians, period, frequency, arc length and tangential speed.

Study this section → The lesson explains lever geometry, signed torque, fixed-axis angular acceleration and constant-angular-acceleration equations.

Study this section → Differentiation and integration link angular kinematics; the dynamics extension gives torque as the angular-momentum rate.

Still needed: Calculus and graph relations are explicit; add a clear rigid-system versus point-object modeling comparison. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Derive the linear/angular links at fixed radius and distinguish shared angular rates from radius-dependent linear quantities.

Essential knowledge checked: 5.2.A.1, 5.2.A.2, 5.2.A.3

Study this section → The lesson connects radians, period, frequency, arc length and tangential speed.

Study this section → The lesson explains lever geometry, signed torque, fixed-axis angular acceleration and constant-angular-acceleration equations.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

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Required depth: Locate the axis, the force line and the perpendicular lever arm before assigning a torque.

Essential knowledge checked: 5.3.A.1, 5.3.A.2

Study this section → The lesson explains lever geometry, signed torque, fixed-axis angular acceleration and constant-angular-acceleration equations.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

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Required depth: Use the torque cross product and its right-hand direction as well as magnitude; retain the application point in the force diagram.

Essential knowledge checked: 5.3.B.1, 5.3.B.2

Study this section → The lesson explains lever geometry, signed torque, fixed-axis angular acceleration and constant-angular-acceleration equations.

Study this section → The particle cross product, origin dependence, rigid-body angular momentum and torque rate are stated.

Study this section → Separate force and moment equations distinguish translational and rotational balance.

Study this section → The component and unit-basis rules, normalized direction vector, dot product and torque cross product are taught. The torque paragraph explicitly applies the right-hand rule; other vector-product applications are optional.

Still needed: The torque vector and right-hand rule are explicit. Add the required extended-body force-diagram drawing convention with forces at their application points. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

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Required depth: Set up inertia integrals using suitable mass elements; required geometries include rods, cylindrical shells, disks and coaxial rings.

Essential knowledge checked: 5.4.A.1, 5.4.A.2, 5.4.A.3, 5.4.A.4

Study this section → Discrete sums, the continuous integral, mass-distribution comparisons and parallel-axis shifts are presented.

Still needed: The integral is stated, but derivations for nonuniform rods, disks and annular/coaxial distributions are not developed in the lesson. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

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Required depth: Use the parallel-axis theorem and develop allowed rod/shell/ring integrals about the stated axes; other solid-body derivations are not assumed.

Essential knowledge checked: 5.4.B.1, 5.4.B.2

Study this section → Discrete sums, the continuous integral, mass-distribution comparisons and parallel-axis shifts are presented.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

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Required depth: Balance torques in one plane and distinguish constant angular velocity from rest and from translational equilibrium.

Essential knowledge checked: 5.5.A.1, 5.5.A.2

Study this section → Separate force and moment equations distinguish translational and rotational balance.

Study this section → The lesson explains lever geometry, signed torque, fixed-axis angular acceleration and constant-angular-acceleration equations.

Still needed: The current equilibrium examples focus on rest; add contrasting cases with constant rotation or translational acceleration. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use fixed-axis inertia and net torque, then combine with an independent translational equation when required.

Essential knowledge checked: 5.6.A.1, 5.6.A.2, 5.6.A.3

Study this section → The lesson explains lever geometry, signed torque, fixed-axis angular acceleration and constant-angular-acceleration equations.

Study this section → The no-slip constraints, instantaneous contact rest and split translational/rotational energy are taught.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

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Required depth: Compare a rigid body’s spin energy with its centre-of-mass translation; do not double-count a point particle’s energy.

Essential knowledge checked: 6.1.A.1, 6.1.A.2, 6.1.A.3

Study this section → Rotational energy and torque-angle work area are explicit; the panel also states the variable-torque integral.

Study this section → The no-slip constraints, instantaneous contact rest and split translational/rotational energy are taught.

Still needed: Add the explicit point-particle equivalence between orbital rotational energy and its translational kinetic energy. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

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Required depth: Integrate variable torque over angle and connect signed graph area to work on a rotating system.

Essential knowledge checked: 6.2.A.1, 6.2.A.2, 6.2.A.3

Study this section → Rotational energy and torque-angle work area are explicit; the panel also states the variable-torque integral.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use the particle cross product and rigid-body inertia relation about a specified reference; compare origin-dependent particle angular momenta.

Essential knowledge checked: 6.3.A.1, 6.3.A.2

Study this section → The particle cross product, origin dependence, rigid-body angular momentum and torque rate are stated.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

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Required depth: Accumulate torque over time, including a variable-torque integral and its signed graphical area.

Essential knowledge checked: 6.3.B.1, 6.3.B.2, 6.3.B.3

Study this section → The particle cross product, origin dependence, rigid-body angular momentum and torque rate are stated.

Still needed: The torque-rate relation is present, but the angular-impulse quantity, finite-interval relation and torque-time area need explicit teaching. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Relate the angular-impulse integral to angular-momentum change and the derivative to torque; use both time-graph representations.

Essential knowledge checked: 6.3.C.1, 6.3.C.2, 6.3.C.3, 6.3.C.4

Study this section → The particle cross product, origin dependence, rigid-body angular momentum and torque rate are stated.

Study this section → Differentiation and integration link angular kinematics; the dynamics extension gives torque as the angular-momentum rate.

Still needed: Add the angular impulse theorem, a torque-time graph and an angular-momentum-time graph; the derivative statement alone does not cover all representations. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Add constituent angular momenta about one common axis and analyze changing inertia without confusing energy conservation.

Essential knowledge checked: 6.4.A.1, 6.4.A.2

Study this section → Zero external torque, changing inertia and internal work are illustrated by rotating systems and central forces.

Study this section → The particle cross product, origin dependence, rigid-body angular momentum and torque rate are stated.

Still needed: Add an explicit internal equal-and-opposite angular-impulse account between the interacting constituents. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

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Required depth: State the axis and system before deciding whether an external torque can change angular momentum.

Essential knowledge checked: 6.4.B.1, 6.4.B.2, 6.4.B.3

Study this section → The particle cross product, origin dependence, rigid-body angular momentum and torque rate are stated.

Study this section → Zero external torque, changing inertia and internal work are illustrated by rotating systems and central forces.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

Practise this objective →

Required depth: Use the centre-of-mass translational term and the spin term about the centre of mass.

Essential knowledge checked: 6.5.A.1

Study this section → The no-slip constraints, instantaneous contact rest and split translational/rotational energy are taught.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

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Required depth: Use no-slip speed/acceleration links and distinguish static contact from dissipative sliding.

Essential knowledge checked: 6.5.B.1, 6.5.B.2

Study this section → The no-slip constraints, instantaneous contact rest and split translational/rotational energy are taught.

Still needed: The lesson gives instantaneous contact rest but should explicitly state why ideal static friction does not dissipate mechanical energy. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Analyze translation and rotation independently while slipping, then reconnect them at the no-slip transition; rolling resistance is outside scope.

Essential knowledge checked: 6.5.C.1, 6.5.C.2

Still needed: Add quantitative slipping dynamics and the dissipative kinetic-friction energy account. The no-slip lesson does not cover this objective. No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Analyze circular and elliptical satellite motion using energy and angular momentum for a dominant central mass, including the escape threshold.

Essential knowledge checked: 6.6.A.1, 6.6.A.2, 6.6.A.3, 6.6.A.4

Study this section → The near-surface and inverse-square energy models are distinguished, including the choice of zero.

Study this section → Zero external torque, changing inertia and internal work are illustrated by rotating systems and central forces.

Study this section → The gravity applications connect local field strength, weight and orbital free fall; the explicit zero-total-energy argument gives escape speed.

Still needed: Add an integrated circular/elliptical energy account and the circular total-energy relation. The gravity applications already explain the zero-energy escape condition. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

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Required depth: Test proportional restoring force and distinguish periodic motion from SHM; use the force law rather than the shape of a potential minimum alone.

Essential knowledge checked: 7.1.A.1, 7.1.A.2

Study this section → The AP-visible generic lesson defines restoring acceleration, period models, phase relationships and amplitude independence.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

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Required depth: Relate angular frequency and period using ideal spring and small-angle pendulum models.

Essential knowledge checked: 7.2.A.1

Study this section → The AP-visible generic lesson defines restoring acceleration, period models, phase relationships and amplitude independence.

Still needed: The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

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Required depth: Use the known sinusoidal ODE solution and derivative relationships, graphs and resonance; proving the general ODE solution is unnecessary.

Essential knowledge checked: 7.3.A.1, 7.3.A.2, 7.3.A.3, 7.3.A.4, 7.3.A.5, 7.3.A.6

Study this section → The AP-visible generic lesson defines restoring acceleration, period models, phase relationships and amplitude independence.

Study this section → The ODE, sinusoidal solution, derivatives and initial conditions are explicit; damping derivations on the same page exceed the core requirement.

Study this section → The driven response explains natural frequency and increased amplitude near resonance.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Use an undamped oscillator’s energy account and amplitude scaling; a local quadratic approximation must be justified before applying it to a nonlinear potential.

Essential knowledge checked: 7.4.A.1, 7.4.A.2, 7.4.A.3, 7.4.A.4

Study this section → The undamped energy budget, displacement and time graphs, and amplitude-squared scaling are taught.

Still needed: No course-matched canonical bank question was verified for this objective.

No practice question has yet been verified for this objective.

Required depth: Linearize restoring torque for small angles and use the rotational equation to obtain a physical-pendulum model; include the torsion analogue.

Essential knowledge checked: 7.5.A.1, 7.5.A.2, 7.5.A.3, 7.5.A.4

Study this section → The AP-visible generic lesson defines restoring acceleration, period models, phase relationships and amplitude independence.

Study this section → The lesson explains lever geometry, signed torque, fixed-axis angular acceleration and constant-angular-acceleration equations.

Study this section → The simple-pendulum paragraphs derive the restoring torque and identify the small-angle limit. The next paragraph constructs a physical pendulum with the parallel-axis theorem. AP Physics 1 needs the simple-pendulum argument only; physical pendulums and amplitude-series corrections are optional there.

Still needed: The physical-pendulum model is derived. Add the torsion-pendulum restoring law and its angular-frequency derivation. The linked practice samples the stated skills; it does not certify all essential-knowledge cases or exam mastery.

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