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 15 cm from the axis of a disc that turns at a steady 200 revolutions per minute. Find its centripetal acceleration a_c.

n = 200 rpmr = 0.15 m

a_c = m/s²

2.Easy

A small object sits 35 cm from the axis of a disc that turns at a steady 300 revolutions per minute. Find its centripetal acceleration a_c.

n = 300 rpmr = 0.35 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 45 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 = 45 mμ_s = 0.3g = 9.81 m/s²

v_max = m/s

4.Medium

A car drives over the top of a hump in the road, which is a circular arc of radius 105 m. Use g = 9.81 m/s². Above what speed v_max do the wheels leave the road at the top?

r = 105 mg = 9.81 m/s²

v_max = m/s

5.Hard

A ball on a string 0.6 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 = 0.6 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 6.5 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 = 6.5 mv₀ = 0

h_min = m

Answer key

1. a_c = 65.8 m/s²
2. a_c = 345.4 m/s²
3. v_max = 11.51 m/s
4. v_max = 32.09 m/s
5. v_min = 2.426 m/s
6. h_min = 16.25 m

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