Formula list

1.1Physical quantities and measurement techniques

1. Resultant of two vectors at right angles

   Supp.

   R = √(x² + y²)

   R

   resultant of the two vectors

   x, y

   the two perpendicular components

   Forces or velocities only. A scale drawing is an accepted method — the syllabus asks for the resultant by calculation or graphically.

1.2Motion

1. Speed

   Core

   v = s / t

   Rearrangeds = vt · t = s / v

   v

   speedm/s

   s

   distance travelledm

   t

   time takens

2. Average speed

   Core

   average speed = total distance travelled / total time taken

   distance

   the whole journeym

   time

   the whole journeys

3. Speed from a distance–time graph

   Core

   speed = gradient of a distance–time graph

   gradient

   rise ÷ run of a straight-line section

4. Distance from a speed–time graph

   Core

   distance travelled = area under a speed–time graph

   area

   of the region between the line and the time axis

   For motion at constant speed or constant acceleration.

5. Acceleration

   Supp.

   a = Δv / t

   RearrangedΔv = at

   a

   accelerationm/s²

   Δv

   change in velocitym/s

   t

   time takens

   A deceleration is a negative acceleration, and is used as such in calculations.

6. Acceleration from a speed–time graph

   Supp.

   acceleration = gradient of a speed–time graph

   gradient

   rise ÷ run

1.3Mass and weight

1. Gravitational field strength

   Core

   g = W / m

   RearrangedW = mg · m = W / g

   g

   gravitational field strengthN/kg

   W

   weightN

   m

   masskg

   The syllabus asks you to know that g is equivalent to the acceleration of free fall.

1.4Density

1. Density

   Core

   ρ = m / V

   Rearrangedm = ρV · V = m / ρ

   ρ

   densityg/cm³, kg/m³

   m

   masskg, g

   V

   volumem³, cm³

1.5.1Effects of forces

1. Resultant force and acceleration

   Supp.

   F = ma

   Rearrangeda = F / m · m = F / a

   F

   resultant forceN

   m

   masskg

   a

   accelerationm/s²

   The force and the acceleration are in the same direction. F = mv²/r is explicitly not required at 0625.

2. Spring constant

   Supp.

   k = F / x

   RearrangedF = kx · x = F / k

   k

   spring constantN/m, N/cm

   F

   force (load)N

   x

   extensionm, cm

   Valid up to the limit of proportionality. An understanding of the elastic limit is not required.

1.5.2Turning effect of forces

1. Moment of a force

   Core

   moment = F × d

   F

   forceN

   d

   perpendicular distance from the pivotm

   moment

   turning effectN m

2. Principle of moments

   Core

   sum of clockwise moments = sum of anticlockwise moments

   about

   the same pivot, for an object in equilibrium

   Core covers one force each side of the pivot; Supplement extends it to more than one force each side.

1.5.3Centre of gravity

No equations. This point is examined through experiment and qualitative reasoning about stability.

1.6Momentum

1. Momentum

   Supp.

   p = mv

   Rearrangedm = p / v · v = p / m

   p

   momentumkg m/s, N s

   m

   masskg

   v

   velocitym/s

2. Impulse

   Supp.

   impulse = FΔt = Δ(mv)

   F

   forceN

   Δt

   time for which the force actss

   Δ(mv)

   change in momentumkg m/s, N s

3. Resultant force from momentum

   Supp.

   F = Δp / Δt

   F

   resultant forceN

   Δp

   change in momentumkg m/s

   Δt

   time takens

4. Conservation of momentum

   Supp.

   total momentum before = total momentum after

   p

   summed for every object, with direction

   Simple problems in one dimension only.

1.7.1Energy

1. Kinetic energy

   Supp.

   Ek = ½mv²

   Rearrangedv = √(2Ek / m)

   Ek

   kinetic energyJ

   m

   masskg

   v

   speedm/s

2. Change in gravitational potential energy

   Supp.

   ΔEp = mgΔh

   ΔEp

   change in g.p.e.J

   m

   masskg

   g

   gravitational field strengthN/kg

   Δh

   change in heightm

3. Conservation of energy

   Core

   total energy before = total energy after

   stores

   kinetic, gravitational potential, chemical, elastic, nuclear, electrostatic, internal

   Core applies this to simple flow diagrams; Supplement to multi-stage examples and Sankey diagrams.

1.7.2Work

1. Mechanical work done

   Core

   W = Fd = ΔE

   RearrangedF = W / d · d = W / F

   W

   work doneJ

   F

   forceN

   d

   distance moved in the direction of the forcem

   ΔE

   energy transferredJ

1.7.3Energy resources

1. Efficiency, by energy

   Supp.

   efficiency = useful energy output / total energy input

   energy

   both terms in the same unitJ

   Multiply by 100% for a percentage. Core needs the idea of efficiency qualitatively; the equation is Supplement.

2. Efficiency, by power

   Supp.

   efficiency = useful power output / total power input

   power

   both terms in the same unitW

   Multiply by 100% for a percentage.

1.7.4Power

1. Power from work done

   Core

   P = W / t

   RearrangedW = Pt · t = W / P

   P

   powerW, kW, MW

   W

   work doneJ

   t

   time takens

2. Power from energy transferred

   Core

   P = ΔE / t

   P

   powerW

   ΔE

   energy transferredJ

   t

   time takens

1.8Pressure

1. Pressure

   Core

   p = F / A

   RearrangedF = pA · A = F / p

   p

   pressureN/m², Pa

   F

   force normal to the surfaceN

   A

   aream², cm²

2. Change in pressure beneath a liquid surface

   Supp.

   Δp = ρgΔh

   Δp

   change in pressurePa

   ρ

   density of the liquidkg/m³

   g

   gravitational field strengthN/kg

   Δh

   change in depthm

2.1.3Gases and the absolute scale of temperature

1. Kelvin and Celsius

   Core

   T (in K) = θ (in °C) + 273

   Rearrangedθ (in °C) = T (in K) − 273

   T

   absolute temperatureK

   θ

   temperature°C

   −273 °C is absolute zero, where particles have least kinetic energy.

2. Pressure and volume of a fixed mass of gas

   Supp.

   pV = constant

   Rearrangedp₁V₁ = p₂V₂

   p

   pressurePa

   V

   volumem³

   For a fixed mass of gas at constant temperature. You may also be asked to represent this graphically.

2.2.2Specific heat capacity

1. Specific heat capacity

   Supp.

   c = ΔE / (mΔθ)

   RearrangedΔE = mcΔθ · Δθ = ΔE / (mc)

   c

   specific heat capacityJ/(kg °C), J/(g °C)

   ΔE

   energy suppliedJ

   m

   masskg, g

   Δθ

   temperature rise°C

2.2.3Melting, boiling and evaporation

No equations. 0625 does not examine specific latent heat — melting, boiling and evaporation are described in terms of energy and particles.

2.3Transfer of thermal energy

No equations. Conduction, convection and radiation are examined qualitatively and through experiment.

3.1General properties of waves

1. Wave speed

   Core

   v = fλ

   Rearrangedf = v / λ · λ = v / f

   v

   wave speedm/s

   f

   frequencyHz, kHz

   λ

   wavelengthm, cm

3.2.1Reflection of light

1. Law of reflection

   Core

   angle of incidence = angle of reflection

   i

   angle of incidence, from the normaldegree (°)

   r

   angle of reflection, from the normaldegree (°)

3.2.2Refraction of light

1. Refractive index from angles

   Supp.

   n = sin i / sin r

   Rearrangedsin r = sin i / n

   n

   refractive index

   i

   angle of incidencedegree (°)

   r

   angle of refractiondegree (°)

2. Refractive index from the critical angle

   Supp.

   n = 1 / sin c

   Rearrangedsin c = 1 / n

   n

   refractive index

   c

   critical angledegree (°)

3. Refractive index as a ratio of speeds

   Supp.

   n = speed in region 1 / speed in region 2

   n

   refractive index

   The syllabus defines refractive index as the ratio of the speeds of a wave in two different regions.

3.2.3Thin lenses

No equations. 0625 examines lenses through ray diagrams and image characteristics — the lens equation is not required.

3.3Electromagnetic spectrum

1. Speed of electromagnetic waves

   Supp.

   c = 3.0 × 10⁸ m/s

   c

   speed in a vacuumm/s

   Approximately the same in air. All electromagnetic waves travel at this speed in a vacuum, which Core candidates must know qualitatively.

3.4Sound

1. Speed of sound by an echo

   DerivedCore

   v = 2d / t

   v

   speed of soundm/s

   d

   distance to the reflecting surfacem

   t

   time for the echo to returns

   Not printed in the syllabus: it is v = s/t with the pulse counted there and back. The syllabus asks for a method involving a measurement of distance and time.

2. Depth or distance from an ultrasound pulse

   DerivedSupp.

   d = vt / 2

   d

   depth or distancem

   v

   wave speed in the mediumm/s

   t

   time for the pulse to returns

   Not printed in the syllabus: it is v = s/t with the pulse counted there and back. The syllabus requires depth or distance to be calculated from time and wave speed for sonar, medical scanning and non-destructive testing.

4.1Simple phenomena of magnetism

No equations. Magnetism at 0625 is field patterns, induced magnetism and the properties of magnetic materials.

4.2.2Electric current

1. Electric current

   Supp.

   I = Q / t

   RearrangedQ = It · t = Q / I

   I

   currentA, mA

   Q

   chargeC

   t

   times

   Conventional current is from positive to negative; free electrons flow from negative to positive.

4.2.3Electromotive force and potential difference

1. Electromotive force

   Supp.

   E = W / Q

   E

   e.m.f.V

   W

   electrical work done by the sourceJ

   Q

   charge moved around the complete circuitC

2. Potential difference

   Supp.

   V = W / Q

   RearrangedW = QV

   V

   potential differenceV, mV, kV

   W

   work done by the charge in the componentJ

   Q

   charge passing throughC

4.2.4Resistance

1. Resistance

   Core

   R = V / I

   RearrangedV = IR · I = V / R

   R

   resistanceΩ

   V

   potential differenceV

   I

   currentA

2. Resistance of a metallic conductor

   Supp.

   R ∝ l · R ∝ 1 / A

   l

   length of the wirem

   A

   cross-sectional aream²

   A proportionality, not a formula: 0625 does not use resistivity. Core candidates state the relationship qualitatively.

4.2.5Electrical energy and electrical power

1. Electrical power

   Core

   P = IV

   RearrangedI = P / V · V = P / I

   P

   powerW, kW

   I

   currentA

   V

   potential differenceV

2. Electrical energy

   Core

   E = IVt

   E

   energy transferredJ, kWh

   I

   currentA

   V

   potential differenceV

   t

   times

   The syllabus also expects the kilowatt-hour to be defined and used to calculate the cost of running an appliance.

4.3.2Series and parallel circuits

1. Resistors in series

   Core

   R = R₁ + R₂ + …

   R

   combined resistanceΩ

2. Cells in series

   Core

   combined e.m.f. = E₁ + E₂ + …

   E

   e.m.f. of each sourceV

3. Current in a series circuit

   Core

   current is the same at every point

   I

   currentA

4. Resistors in parallel

   Supp.

   1 / R = 1 / R₁ + 1 / R₂

   R

   combined resistanceΩ

   Two resistors. The combined resistance is always less than either resistor alone — which Core candidates state without calculating.

5. Currents at a junction

   Supp.

   sum of currents in = sum of currents out

   I

   current in each branchA

6. Potential differences in a series circuit

   Supp.

   total p.d. = V₁ + V₂ + …

   V

   p.d. across each componentV

   Across parallel branches the p.d. is the same as across any one branch.

4.3.3Action and use of circuit components

1. Two resistors as a potential divider

   Supp.

   R₁ / R₂ = V₁ / V₂

   R₁, R₂

   the two resistancesΩ

   V₁, V₂

   the p.d. across eachV

4.4Electrical safety

No new equations. Fuse ratings and trip settings are chosen using P = IV from 4.2.5.

4.5.6The transformer

1. Transformer turns and voltage

   Core

   Vp / Vs = Np / Ns

   Vp, Vs

   primary and secondary p.d.V

   Np, Ns

   turns on primary and secondary coils

2. Transformer at 100% efficiency

   Supp.

   IpVp = IsVs

   Ip, Is

   primary and secondary currentA

   Vp, Vs

   primary and secondary p.d.V

3. Power loss in transmission cables

   Supp.

   P = I²R

   P

   power dissipated in the cableW

   I

   currentA

   R

   resistance of the cableΩ

   Used to explain why losses are smaller when transmission voltage is greater.

5.1.2The nucleus

1. Nuclide notation

   Core

   ᴬZX

   A

   nucleon number (mass number)

   Z

   proton number (atomic number)

   X

   chemical symbol of the element

2. Number of neutrons

   Core

   number of neutrons = A − Z

   A

   nucleon number

   Z

   proton number

5.2.1Detection of radioactivity

1. Corrected count rate

   Supp.

   corrected count rate = measured count rate − background count rate

   count rate

   counts per second or per minutecounts/s, counts/min

5.2.3Radioactive decay

1. Alpha decay

   Supp.

   A decreases by 4 · Z decreases by 2

   α

   an alpha particle is a helium nucleus, ⁴₂He

   Written as a decay equation in nuclide notation.

2. Beta decay

   Supp.

   A unchanged · Z increases by 1

   β

   a beta particle is an electron, ⁰₋₁e

   In the nucleus: neutron → proton + electron. β⁺ is not included; β means β⁻.

3. Gamma emission

   Supp.

   A unchanged · Z unchanged

   γ

   electromagnetic radiation from the nucleus

5.2.4Half-life

1. Half-life

   Core

   half-life = time for half the nuclei of an isotope to decay

   t½

   half-lifes, min, h, days, weeks, years

   Calculations at Core will not include background radiation; Supplement calculates half-life from decay curves that still contain it.

2. Fraction remaining after n half-lives

   DerivedCore

   fraction remaining = (½)ⁿ

   n

   number of half-lives elapsed

   Not printed in the syllabus: it is the definition of half-life applied repeatedly, and it is how most half-life questions are answered.

6.1.1The Earth

1. Average orbital speed

   Supp.

   v = 2πr / T

   v

   average orbital speedm/s

   r

   average radius of the orbitm

   T

   orbital periods

6.1.2The Solar System

1. Travel time of light

   DerivedCore

   t = d / c

   t

   time takens

   d

   distancem

   c

   speed of lightm/s

   Not printed in the syllabus: it is v = s/t. The syllabus asks you to calculate the time light takes to cross Solar System distances.

6.2.2Stars

1. Light-year

   Supp.

   1 light-year = 9.5 × 10¹⁵ m

   ly

   distance light travels in one year in a vacuumm

   Core candidates define the light-year without being given the value.

6.2.3The Universe

1. Hubble constant

   Supp.

   H₀ = v / d

   Rearrangedv = H₀d · d = v / H₀

   H₀

   Hubble constants⁻¹

   v

   speed the galaxy is receding atm/s

   d

   distance of the galaxy from Earthm

2. Estimated age of the Universe

   Supp.

   d / v = 1 / H₀

   1 / H₀

   an estimate of the age of the Universes

   Evidence for all the matter in the Universe having once been at a single point.