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 1600 kg car drives around a flat curve of radius 30 m at a constant 9 m/s. Find its centripetal acceleration a_c.

m = 1600 kgv = 9 m/sr = 30 m

a_c = m/s²

3.Medium

A 1300 kg car drives over the top of a hump in the road at 13 m/s. The top of the hump is a circular arc of radius 35 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1300 kgv = 13 m/sr = 35 mg = 9.81 m/s²

N = N

4.Medium

A car takes a flat curve of radius 110 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 = 110 mμ_s = 0.4g = 9.81 m/s²

v_max = m/s

5.Hard

A 2 kg ball on a string 1.1 m long is swung in a vertical circle. At the lowest point it moves at 4 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 2 kgr = 1.1 mv = 4 m/sg = 9.81 m/s²

T = N

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. r_min = 5556 m
2. a_c = 2.7 m/s²
3. N = 6476 N
4. v_max = 20.78 m/s
5. T = 48.71 N
6. v_min = 2.215 m/s

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