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 25 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 = 0.25 m

a_c = m/s²

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 2 m/s². What is the smallest radius r_min for a curve taken at 300 km/h?

v = 300 km/ha_max = 2 m/s²

r_min = m

3.Medium

A car takes a flat curve of radius 150 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 = 150 mμ_s = 0.7g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 70 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 = 70 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

5.Hard

A ball on a string 1.2 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 = 1.2 mg = 9.81 m/s²

v_min = m/s

6.Hard

A curve of radius 270 m is banked at 18°, and 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 a car can take the curve without sliding up and out.

r = 270 mθ = 18°μ_s = 0.3g = 9.81 m/s²

v_max = m/s

Answer key

1. a_c = 109.7 m/s²
2. r_min = 3472 m
3. v_max = 32.09 m/s
4. v_max = 18.53 m/s
5. v_min = 3.431 m/s
6. v_max = 42.83 m/s

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