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

For passenger comfort the centripetal acceleration on a railway curve must not exceed 2 m/s². What is the smallest radius r_min for a curve taken at 240 km/h?

v = 240 km/ha_max = 2 m/s²

r_min = m

3.Medium

A car drives over the top of a hump in the road, which is a circular arc of radius 85 m. Use g = 9.81 m/s². Above what speed v_max do the wheels leave the road at the top?

r = 85 mg = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 115 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 = 115 mμ_s = 0.7g = 9.81 m/s²

v_max = m/s

5.Hard

A 1.8 kg ball on a string 0.7 m long is swung in a vertical circle. At the lowest point it moves at 6.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.8 kgr = 0.7 mv = 6.5 m/sg = 9.81 m/s²

T = N

6.Hard

A 1 kg ball on a string 0.6 m long is swung in a vertical circle. At the lowest point it moves at 9 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1 kgr = 0.6 mv = 9 m/sg = 9.81 m/s²

T = N

Answer key

1. r_min = 5556 m
2. r_min = 2222 m
3. v_max = 28.88 m/s
4. v_max = 28.1 m/s
5. T = 126.3 N
6. T = 144.8 N

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