Circular motion worksheet with answers

Free printable Circular motion worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A 900 kg car drives around a flat curve of radius 150 m at a constant 29 m/s. Find its centripetal acceleration a_c.

m = 900 kgv = 29 m/sr = 150 m

a_c = m/s²

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.5 m/s². What is the smallest radius r_min for a curve taken at 200 km/h?

v = 200 km/ha_max = 1.5 m/s²

r_min = m

3.Medium

A small ball on a string of length 1.7 m moves in a horizontal circle so that the string makes a constant angle of 60° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 1.7 mθ = 60°g = 9.81 m/s²

v = m/s

4.Medium

A small ball on a string of length 0.7 m moves in a horizontal circle so that the string makes a constant angle of 30° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 0.7 mθ = 30°g = 9.81 m/s²

v = m/s

5.Hard

A curve of radius 40 m is banked at 30°, and the coefficient of static friction between tyres and road is 0.15. Use g = 9.81 m/s². Find the highest speed v_max at which a car can take the curve without sliding up and out.

r = 40 mθ = 30°μ_s = 0.15g = 9.81 m/s²

v_max = m/s

6.Hard

A ball on a string 0.5 m long is swung in a vertical circle. Use g = 9.81 m/s². What is the smallest speed v_min at the top for which the string just stays tight?

r = 0.5 mg = 9.81 m/s²

v_min = m/s

Answer key

1. a_c = 5.607 m/s²
2. r_min = 2058 m
3. v = 5.002 m/s
4. v = 1.408 m/s
5. v_max = 17.68 m/s
6. v_min = 2.215 m/s

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