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 0.8 m/s². What is the smallest radius r_min for a curve taken at 240 km/h?

v = 240 km/ha_max = 0.8 m/s²

r_min = m

2.Easy

A small object sits 45 cm from the axis of a disc that turns at a steady 30 revolutions per minute. Find the speed v of the object.

n = 30 rpmr = 0.45 m

v = m/s

3.Medium

A curve of radius 390 m is banked at 18°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 390 mθ = 18°g = 9.81 m/s²

v = m/s

4.Medium

A car takes a flat curve of radius 80 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 = 80 mμ_s = 0.4g = 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 curve of radius 170 m is banked at 20°, and the coefficient of static friction between tyres and road is 0.2. 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 = 170 mθ = 20°μ_s = 0.2g = 9.81 m/s²

v_max = m/s

Answer key

1. r_min = 5556 m
2. v = 1.414 m/s
3. v = 35.26 m/s
4. v_max = 17.72 m/s
5. v_min = 2.215 m/s
6. v_max = 31.85 m/s

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