Quick answer: Uniform circular motion is travel at constant speed along a circle. This AP Physics 1 worksheet on centripetal acceleration gives 20 problems from easy to hard: direction check, track cycling and record player. The worked answers are on a separate page, and the worksheet is a free printable PDF.
These twenty problems build circular motion and gravitation skills in the style of AP Physics 1 unit 2. They start with direction and scaling reasoning, move to calculations with a = v²/r and F = G m₁ m₂ / r², and end with free-response tasks that mix equations with written justification.
Use g = 9.81 m/s², G = 6.67 × 10⁻¹¹ N m²/kg² and show every substitution. Where a problem asks you to explain, write full sentences that link forces to the acceleration.
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 2
Problem 1 Direction check ★★★
Answer about an object moving at constant speed on a horizontal circle.1. State the direction of its acceleration.
2. State the direction of the net force on it.
3. Explain why its speed stays constant even though it accelerates.
Problem 2 Track cycling ★★★
Bilal in Lahore rides at a steady 7.2 m/s round a circular track of radius 24 m. The total mass of Bilal and the bicycle is 80 kg.1. Calculate his centripetal acceleration.
2. Calculate the net force on him.
3. Calculate the time for one lap.
Problem 3 Record player ★★★
A small mark sits 0.12 m from the centre of a record turning at 45 revolutions per minute.1. Calculate the period in seconds.
2. Calculate the speed of the mark.
3. Calculate its centripetal acceleration.
Problem 4 Scaling the pull ★★★
The gravitational force between two planets is F. State the new force in terms of F when:1. the distance between them is halved.
2. one mass is tripled and the distance is tripled.
3. both masses are doubled and the distance is doubled.
Problem 5 Two cargo ships ★★★
Two cargo ships, each of mass 5.0 × 10⁷ kg, lie 200 m apart in a calm harbour. Use G = 6.67 × 10⁻¹¹ N m²/kg².1. Calculate the gravitational force between them.
2. Explain why the ships do not drift together.
Problem 6 Real forces only ★★★
Name the single real force, or the combination of forces, that provides the centripetal force in each case.1. A coin riding on a turntable without slipping.
2. A conker swung round on a string above the head.
3. A satellite orbiting the Earth.
4. A rider pressed against the wall of a spinning drum.
Problem 7 Coin on a turntable ★★★
A coin rests on a horizontal turntable at 0.080 m from the axis, as shown. The coefficient of static friction is 0.45. Use g = 9.81 m/s².1. State which force provides the centripetal force.
2. Show that the greatest speed without slipping is v = √(μs g r) and calculate it.
3. Calculate the greatest rate of turning in revolutions per minute.
Problem 8 Rover on Mars ★★★
Mars has mass 6.42 × 10²³ kg and radius 3.39 × 10⁶ m. Use G = 6.67 × 10⁻¹¹ N m²/kg². A rover of mass 180 kg stands on the surface.1. Calculate the gravitational field strength at the surface of Mars.
2. Calculate the weight of the rover on Mars.
3. Compare that weight with its weight on Earth.
Problem 9 Orbit of Europa ★★★
The moon Europa moves on a nearly circular orbit of radius 6.71 × 10⁸ m around Jupiter, mass 1.90 × 10²⁷ kg. Use G = 6.67 × 10⁻¹¹ N m²/kg².1. Calculate its orbital speed.
2. Calculate its period in days.
3. State how the answers would change for a moon of twice the mass at the same radius.
Problem 10 Swinging a bucket ★★★
Wanjiru in Nairobi swings a 1.5 kg bucket of water in a vertical circle of radius 0.90 m. Use g = 9.81 m/s².1. Calculate the least speed at the top for the water to stay in the bucket.
2. Calculate the force in the rope at the bottom when the speed there is 5.0 m/s.
Problem 11 Reading a straight line ★★★
A student measures centripetal acceleration for several speeds on one fixed circle and plots the graph.1. Explain why the graph is a straight line through the origin.
2. Use the gradient to find the radius of the circle.
3. Predict ac when v = 8.0 m/s.
Problem 12 Comparing two orbits ★★★
Satellite B orbits the same planet as satellite A, at four times the orbital radius. Both are in circular orbits. Give each ratio B : A.1. Orbital speed.
2. Period.
3. Centripetal acceleration.
Problem 13 Spot the slip ★★★
A student writes: “A 900 kg car takes a bend of radius 50 m at 20 m/s, so the centripetal force is m v / r = 900 × 20 ÷ 50 = 360 N.”1. Identify the mistake.
2. Calculate the correct force.
Problem 14 Floating in orbit ★★★
A space station orbits 400 km above the surface of the Earth. Use G M = 3.98 × 10¹⁴ m³/s² and Earth radius 6.37 × 10⁶ m.1. Calculate the gravitational field strength at the station.
2. Express it as a percentage of the surface value, 9.81 N/kg.
3. Explain why astronauts nevertheless float.
Problem 15 Tractor on a farm track ★★★
A tractor takes a level, curved farm track of radius 35 m. Use g = 9.81 m/s².1. Calculate the greatest speed on dry soil, where μs = 0.60.
2. Calculate the greatest speed after rain, where μs = 0.25.
3. Explain, using forces, why the safe speed falls.
Problem 16 Ferris wheel rider ★★★
Mei rides a Ferris wheel of radius 12 m that turns once every 30 s at constant speed. Her mass is 55 kg. Use g = 9.81 m/s².1. Calculate her speed and centripetal acceleration.
2. Calculate the normal force from the seat at the top.
3. Calculate the normal force at the bottom.
4. Explain, using the free-body diagrams, why she feels lightest at the top.
Problem 17 Satellite that stays overhead ★★★
A communications satellite stays above one point on the equator. Its period is 24 h = 86 400 s. Use G M = 3.98 × 10¹⁴ m³/s² and Earth radius 6.37 × 10⁶ m.1. Derive T² = 4π² r³ / (G M) from the force equation.
2. Calculate the orbit radius.
3. Calculate its height above the surface and its speed.
Problem 18 Bigger planet, same mass ★★★
A planet has the same mass as the Earth but twice the radius.1. Predict qualitatively whether the surface gravity is greater or smaller than on Earth.
2. Derive the ratio gplanet / gEarth from g = G M / r².
3. Derive the ratio of the speeds of satellites skimming each surface.
4. Write a short paragraph arguing which world needs the greater launch speed to reach a skimming orbit, and why.
Problem 19 Design: force against period ★★★
Design an experiment to test the relationship between the tension in a string and the period of a rubber bung of mass 0.200 kg swung in a horizontal circle of radius 0.50 m. Write answers for:1. The independent and dependent variables and two controls.
2. The measurements and equipment.
3. The graph to plot so that the relationship is a straight line, and what its gradient should equal.
4. One source of error and how to reduce it.
Problem 20 Double asteroid ★★★
Two asteroids, each of mass 8.0 × 10¹¹ kg, orbit the midpoint between them while their centres stay 2.0 km apart. Use G = 6.67 × 10⁻¹¹ N m²/kg².1. State the radius of each orbit.
2. Show that the speed of each asteroid is v = √(G m / (2d)).
3. Calculate that speed and the period in hours.
