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Cambridge International AS & A Level · 12 · structured

Radians and the direction-changing force

Radians and the direction-changing force · Original GioPhysics question with a detailed, mark-by-mark answer guide.

Demand
demanding
Marks
7
Topics
4
Answer
Complete
structured7 marks

A 0.30 kg object travels at constant speed 4.0 m s⁻¹ in a circle of radius 0.80 m. Use the following parts to explain its motion; do not add a separate 'centripetal force' to a force already supplying the inward resultant.

  1. (a)

    Define one radian. Find the angular displacement when the object travels an arc length of 1.20 m.

    2 marks
  2. (b)

    Explain why a constant-magnitude resultant force always perpendicular to the velocity changes direction without changing speed. State its direction in this circular motion and why angular speed is constant.

    3 marks
  3. (c)

    Recall both forms of centripetal acceleration and calculate its magnitude here.

    2 marks
Ready to self-mark?Reveal the detailed answer guide
Answer overview(a) One radian subtends arc length equal to radius; θ = 1.50 rad. (b) The force does no work instantaneously, changes velocity direction, points inward, and fixed v and r give constant ω=v/r. (c) a = v²/r = rω² = 20 m s⁻².
01

(a)

2 marks

Define one radian. Find the angular displacement when the object travels an arc length of 1.20 m.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    A central angle is one radian when its arc length equals the radius.

  2. 2

    θ = s/r = 1.20/0.80 = 1.50 rad.

02

(b)

3 marks

Explain why a constant-magnitude resultant force always perpendicular to the velocity changes direction without changing speed. State its direction in this circular motion and why angular speed is constant.

How to approach it

Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.

  1. 1

    A perpendicular force has no component along instantaneous motion, so it does not transfer kinetic energy and speed stays constant.

  2. 2

    Its inward action continuously turns the velocity towards the centre.

  3. 3

    Since v and r are constant, ω=v/r is constant; centripetal acceleration is compatible with uniform angular speed.

03

(c)

2 marks

Recall both forms of centripetal acceleration and calculate its magnitude here.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    State a=v²/r=rω².

  2. 2

    Use a=4.0²/0.80=20 m s⁻², towards the centre.

Complete marking guidance

Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.

  1. (a) A central angle is one radian when its arc length equals the radius.
  2. (a) θ = s/r = 1.20/0.80 = 1.50 rad.
  3. (b) A perpendicular force has no component along instantaneous motion, so it does not transfer kinetic energy and speed stays constant.
  4. (b) Its inward action continuously turns the velocity towards the centre.
  5. (b) Since v and r are constant, ω=v/r is constant; centripetal acceleration is compatible with uniform angular speed.
  6. (c) State a=v²/r=rω².
  7. (c) Use a=4.0²/0.80=20 m s⁻², towards the centre.

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