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 200 km/h?

v = 200 km/ha_max = 1 m/s²

r_min = m

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.5 m/s². What is the smallest radius r_min for a curve taken at 240 km/h?

v = 240 km/ha_max = 1.5 m/s²

r_min = m

3.Medium

A car takes a flat curve of radius 55 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 = 55 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

4.Medium

A 1600 kg car drives over the top of a hump in the road at 6 m/s. The top of the hump is a circular arc of radius 45 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1600 kgv = 6 m/sr = 45 mg = 9.81 m/s²

N = N

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 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

Answer key

1. r_min = 3086 m
2. r_min = 2963 m
3. v_max = 16.42 m/s
4. N = 14416 N
5. v_min = 3.431 m/s
6. v_min = 2.62 m/s

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