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 160 km/h?

v = 160 km/ha_max = 1.5 m/s²

r_min = m

2.Easy

An 800 kg car drives around a flat curve of radius 80 m at a constant 12 m/s. Find its centripetal acceleration a_c.

m = 800 kgv = 12 m/sr = 80 m

a_c = m/s²

3.Medium

A small ball on a string of length 0.8 m moves in a horizontal circle so that the string makes a constant angle of 45° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 0.8 mθ = 45°g = 9.81 m/s²

v = m/s

4.Medium

A car takes a flat curve of radius 140 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 140 mμ_s = 0.4g = 9.81 m/s²

v_max = m/s

5.Hard

A 0.5 kg cart is released from rest at a height of 38 m on a frictionless track and runs through a vertical loop of radius 9.5 m. Use g = 9.81 m/s². Find the normal force N_top of the track on the cart at the top of the loop.

m = 0.5 kgh = 38 mR = 9.5 mg = 9.81 m/s²

N_top = N

6.Hard

A ball on a string 1.3 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 = 1.3 mg = 9.81 m/s²

v_min = m/s

Answer key

1. r_min = 1317 m
2. a_c = 1.8 m/s²
3. v = 2.356 m/s
4. v_max = 23.44 m/s
5. N_top = 14.71 N
6. v_min = 3.571 m/s

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