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 1 m/s². What is the smallest radius r_min for a curve taken at 160 km/h?

v = 160 km/ha_max = 1 m/s²

r_min = m

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.2 m/s². What is the smallest radius r_min for a curve taken at 160 km/h?

v = 160 km/ha_max = 1.2 m/s²

r_min = m

3.Medium

A curve of radius 130 m is banked at 15°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 130 mθ = 15°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 0.7. 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 = 0.7g = 9.81 m/s²

v_max = m/s

5.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

6.Hard

A curve of radius 210 m is banked at 25°, 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 = 210 mθ = 25°μ_s = 0.2g = 9.81 m/s²

v_max = m/s

Answer key

1. r_min = 1975 m
2. r_min = 1646 m
3. v = 18.49 m/s
4. v_max = 23.44 m/s
5. v_min = 2.62 m/s
6. v_max = 38.91 m/s

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