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 85 cm from the axis of a disc that turns at a steady 30 revolutions per minute. Find its centripetal acceleration a_c.

n = 30 rpmr = 0.85 m

a_c = m/s²

2.Easy

A small object sits 125 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 = 1.25 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 40 m. The coefficient of static friction between tyres and road is 0.8. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 40 mμ_s = 0.8g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 25 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 = 25 mμ_s = 0.7g = 9.81 m/s²

v_max = m/s

5.Hard

A ball on a string 0.5 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 = 0.5 mg = 9.81 m/s²

v_min = m/s

6.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

Answer key

1. a_c = 8.389 m/s²
2. a_c = 548.3 m/s²
3. v_max = 17.72 m/s
4. v_max = 13.1 m/s
5. v_min = 2.215 m/s
6. v_min = 2.62 m/s

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