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 1000 kg car drives around a flat curve of radius 160 m at a constant 18 m/s. Find its centripetal acceleration a_c.

m = 1000 kgv = 18 m/sr = 160 m

a_c = m/s²

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.5 m/s². What is the smallest radius r_min for a curve taken at 160 km/h?

v = 160 km/ha_max = 1.5 m/s²

r_min = m

3.Medium

A car takes a flat curve of radius 90 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 = 90 mμ_s = 0.7g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 65 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 = 65 mμ_s = 0.3g = 9.81 m/s²

v_max = m/s

5.Hard

A curve of radius 50 m is banked at 15°, and the coefficient of static friction between tyres and road is 0.15. 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 = 50 mθ = 15°μ_s = 0.15g = 9.81 m/s²

v_max = m/s

6.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

Answer key

1. a_c = 2.025 m/s²
2. r_min = 1317 m
3. v_max = 24.86 m/s
4. v_max = 13.83 m/s
5. v_max = 14.61 m/s
6. v_min = 2.215 m/s

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