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 1600 kg car drives around a flat curve of radius 90 m at a constant 26 m/s. Find its centripetal acceleration a_c.

m = 1600 kgv = 26 m/sr = 90 m

a_c = m/s²

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.2 m/s². What is the smallest radius r_min for a curve taken at 120 km/h?

v = 120 km/ha_max = 1.2 m/s²

r_min = m

3.Medium

A car takes a flat curve of radius 90 m. The coefficient of static friction between tyres and road is 0.7. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 90 mμ_s = 0.7g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 65 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 = 65 mμ_s = 0.3g = 9.81 m/s²

v_max = m/s

5.Hard

A ball on a string 0.7 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 = 0.7 mg = 9.81 m/s²

v_min = m/s

6.Hard

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 5.5 m. From what minimum height h_min above the bottom of the loop must it start to stay on the track at the top of the loop?

R = 5.5 mv₀ = 0

h_min = m

Answer key

1. a_c = 7.511 m/s²
2. r_min = 925.9 m
3. v_max = 24.86 m/s
4. v_max = 13.83 m/s
5. v_min = 2.62 m/s
6. h_min = 13.75 m

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