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 140 cm from the axis of a disc that turns at a steady 150 revolutions per minute. Find its centripetal acceleration a_c.

n = 150 rpmr = 1.4 m

a_c = m/s²

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.5 m/s². What is the smallest radius r_min for a curve taken at 250 km/h?

v = 250 km/ha_max = 0.5 m/s²

r_min = m

3.Medium

A car takes a flat curve of radius 55 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 = 55 mμ_s = 0.7g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 120 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 = 120 mμ_s = 0.4g = 9.81 m/s²

v_max = m/s

5.Hard

A ball on a string 0.9 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 = 0.9 mg = 9.81 m/s²

v_min = m/s

6.Hard

A 1 kg ball on a string 1.4 m long is swung in a vertical circle. At the lowest point it moves at 8 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1 kgr = 1.4 mv = 8 m/sg = 9.81 m/s²

T = N

Answer key

1. a_c = 345.4 m/s²
2. r_min = 9645 m
3. v_max = 19.43 m/s
4. v_max = 21.7 m/s
5. v_min = 2.971 m/s
6. T = 55.52 N

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