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S6 Physics: Circular Motion and Gravitation – Practice Paper 1 (Foundation, 10 Questions)
S6 Physics: Circular Motion and Gravitation – Practice Paper 1 (Foundation, 10 Questions)
Paper one links the four basic quantities of circular motion: period, frequency, angular speed, speed and centripetal acceleration, then uses the centripetal force for a turntable and a car on a bend, moves on to surface gravity from Newton law of gravitation, and finishes with the direction of acceleration and the error of treating the centripetal force as an extra force.
Quick answer v = 2 pi r over T, about 3.14 m/s; a = 16 over 0.5 is 32 m/s squared; F = 18 over 1.5 is 12 N; 60 rpm means 1 Hz, T = 1 s and 6.28 rad/s; 2 Hz gives 10.1 m/s and 126 m/s squared; a 1200 kg car needs 9600 N; surface g is about 9.77 m/s squared; four radii give one sixteenth, about 0.61 m/s squared; constant speed still has acceleration because the direction changes; the centripetal force is not an extra force.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 questions |
| Suggested time | about 25 minutes |
| Difficulty mix | Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1 |
| Chapter | Chapter: S6 Physics | Circular Motion and Gravitation: Centripetal Force, Angular Speed and Orbital Period |
| Level | S6 |
02 Questions (10 items)
- FoundationA body moves on a circular track of radius 2 m with a period of 4 s. Find its speed.
- FoundationA body moves at 4 m/s on a circle of radius 0.5 m. What is its centripetal acceleration?
- FoundationA 2 kg body moves at 3 m/s on a circle of radius 1.5 m. What centripetal force is needed?
- FoundationA turntable spins at 60 rpm. Find its frequency, period and angular speed.
- IntermediateA body moves at 2 Hz on a circle of radius 0.8 m. Find its speed and centripetal acceleration.
- IntermediateA 1200 kg car takes a bend of radius 50 m at 20 m/s. What centripetal force is required?
- IntermediateThe Earth has mass 6.0 times 10 to the 24 kg and radius 6.4 times 10 to the 6 m. Find the gravitational field strength at its surface.
- ChallengeA satellite orbits at four Earth radii from the Earth centre. What fraction of the surface gravity does it feel?
- ChallengeThe speed in circular motion is constant, so why is there still an acceleration?
- Error redoA student says the centripetal force is an extra force that a body possesses. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | v = 2 pi r / T = 2 pi times 2 divided by 4, which is pi, about 3.14 m/s | The speed in circular motion is the circumference divided by the period. |
| 2 | a = v squared over r = 16 divided by 0.5, which is 32 m/s squared, directed towards the centre | Centripetal acceleration grows with the square of the speed and falls as the radius grows. |
| 3 | F = m v squared over r = 2 times 9 divided by 1.5, which is 12 N towards the centre | The centripetal force is a net force, not an extra kind of force. |
| 4 | f = 60 divided by 60 = 1 Hz; T = 1 s; angular speed = 2 pi, about 6.28 rad/s | rpm means revolutions per minute, so convert to revolutions per second before using the formulas. |
| 5 | T = 0.5 s; v = 2 pi times 0.8 divided by 0.5, about 10.1 m/s; a = v squared over r, about 126 m/s squared | Convert the frequency to a period first, then apply the speed and acceleration formulas. |
| 6 | F = 1200 times 400 divided by 50, which is 9600 N, supplied by friction between the tyres and the road | The centripetal force is supplied by a real force, here friction at the tyres. |
| 7 | g = GM over R squared = 6.67 times 10 to the minus 11 times 6.0 times 10 to the 24, divided by 6.4 times 10 to the 6 squared, about 9.77 m/s squared | Surface gravity depends only on the mass and radius of the body. |
| 8 | Gravity falls as the inverse square, so four times the distance gives one sixteenth: 9.8 divided by 16, about 0.61 m/s squared | Measure the distance from the centre of the Earth, not from its surface. |
| 9 | Velocity is a vector and its direction keeps changing; acceleration is the rate of change of velocity, so it is non-zero, points to the centre and has magnitude v squared over r | Uniform circular motion means uniform speed only, not uniform velocity. |
| 10 | The centripetal force is not a new force: it is supplied by the radial component of existing forces such as tension, weight, friction or a normal force, and the name only describes the direction of the net force | Treating the centripetal force as a separate force is the commonest mistake in free-body diagrams. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
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