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 240 km/h?

v = 240 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 200 km/h?

v = 200 km/ha_max = 1.5 m/s²

r_min = m

3.Medium

A 1600 kg car drives over the top of a hump in the road at 24 m/s. The top of the hump is a circular arc of radius 90 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1600 kgv = 24 m/sr = 90 mg = 9.81 m/s²

N = N

4.Medium

A small ball on a string of length 0.6 m moves in a horizontal circle so that the string makes a constant angle of 20° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 0.6 mθ = 20°g = 9.81 m/s²

T = s

5.Hard

A 1.1 kg ball on a string 0.9 m long is swung in a vertical circle. At the lowest point it moves at 5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.1 kgr = 0.9 mv = 5 m/sg = 9.81 m/s²

T = N

6.Hard

A 1.7 kg ball on a string 1.3 m long is swung in a vertical circle. At the lowest point it moves at 5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.7 kgr = 1.3 mv = 5 m/sg = 9.81 m/s²

T = N

Answer key

1. r_min = 4444 m
2. r_min = 2058 m
3. N = 5456 N
4. T = 1.506 s
5. T = 41.35 N
6. T = 49.37 N

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