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 600 kg car drives around a flat curve of radius 30 m at a constant 20 m/s. Find its centripetal acceleration a_c.

m = 600 kgv = 20 m/sr = 30 m

a_c = m/s²

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.5 m/s². What is the smallest radius r_min for a curve taken at 240 km/h?

v = 240 km/ha_max = 0.5 m/s²

r_min = m

3.Medium

A car takes a flat curve of radius 70 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 = 70 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 105 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 105 mμ_s = 0.6g = 9.81 m/s²

v_max = m/s

5.Hard

A 0.9 kg ball on a string 1 m long is swung in a vertical circle. At the lowest point it moves at 6 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.9 kgr = 1 mv = 6 m/sg = 9.81 m/s²

T = N

6.Hard

A 0.4 kg ball on a string 0.8 m long is swung in a vertical circle. At the lowest point it moves at 8 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.4 kgr = 0.8 mv = 8 m/sg = 9.81 m/s²

T = N

Answer key

1. a_c = 13.33 m/s²
2. r_min = 8889 m
3. v_max = 18.53 m/s
4. v_max = 24.86 m/s
5. T = 41.23 N
6. T = 35.92 N

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