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 small object sits 65 cm from the axis of a disc that turns at a steady 120 revolutions per minute. Find its centripetal acceleration a_c.

n = 120 rpmr = 0.65 m

a_c = m/s²

2.Easy

A 1100 kg car drives around a flat curve of radius 200 m at a constant 26 m/s. Find the inward (centripetal) force F_c needed.

m = 1100 kgv = 26 m/sr = 200 m

F_c = N

3.Medium

A car takes a flat curve of radius 30 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 = 30 mμ_s = 0.3g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 95 m. The coefficient of static friction between tyres and road is 0.5. 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 = 0.5g = 9.81 m/s²

v_max = m/s

5.Hard

A ball on a string 1.1 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 = 1.1 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 1.5 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 = 1.5 mv₀ = 0

h_min = m

Answer key

1. a_c = 102.6 m/s²
2. F_c = 3718 N
3. v_max = 9.396 m/s
4. v_max = 21.59 m/s
5. v_min = 3.285 m/s
6. h_min = 3.75 m

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