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

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 120 km/h?

v = 120 km/ha_max = 0.5 m/s²

r_min = m

2.Easy

A small object sits 80 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 = 0.8 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 125 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 = 125 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 130 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 = 130 mμ_s = 0.3g = 9.81 m/s²

v_max = m/s

5.Hard

A curve of radius 60 m is banked at 18°, and 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 a car can take the curve without sliding up and out.

r = 60 mθ = 18°μ_s = 0.4g = 9.81 m/s²

v_max = m/s

6.Hard

A ball on a string 1.3 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 = 1.3 mg = 9.81 m/s²

v_min = m/s

Answer key

1. r_min = 2222 m
2. a_c = 7.896 m/s²
3. v_max = 24.76 m/s
4. v_max = 19.56 m/s
5. v_max = 22.15 m/s
6. v_min = 3.571 m/s

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