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

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 120 km/h?

v = 120 km/ha_max = 1.5 m/s²

r_min = m

2.Easy

A 700 kg car drives around a flat curve of radius 80 m at a constant 9 m/s. Find the inward (centripetal) force F_c needed.

m = 700 kgv = 9 m/sr = 80 m

F_c = N

3.Medium

A car takes a flat curve of radius 95 m. The coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 95 mμ_s = 0.3g = 9.81 m/s²

v_max = m/s

4.Medium

A small ball on a string of length 1.9 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 = 1.9 mθ = 30°g = 9.81 m/s²

v = m/s

5.Hard

A curve of radius 110 m is banked at 12°, and the coefficient of static friction between tyres and road is 0.1. Use g = 9.81 m/s². Find the lowest speed v_min at which a car can take the curve without sliding down the bank.

r = 110 mθ = 12°μ_s = 0.1g = 9.81 m/s²

v_min = m/s

6.Hard

A ball on a string 0.9 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 = 0.9 mg = 9.81 m/s²

v_min = m/s

Answer key

1. r_min = 740.7 m
2. F_c = 708.8 N
3. v_max = 16.72 m/s
4. v = 2.32 m/s
5. v_min = 10.91 m/s
6. v_min = 2.971 m/s

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