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 1400 kg car drives around a flat curve of radius 180 m at a constant 9 m/s. Find its centripetal acceleration a_c.

m = 1400 kgv = 9 m/sr = 180 m

a_c = m/s²

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 120 km/h?

v = 120 km/ha_max = 2 m/s²

r_min = m

3.Medium

A car takes a flat curve of radius 75 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 = 75 mμ_s = 0.7g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 60 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 = 60 mμ_s = 0.7g = 9.81 m/s²

v_max = m/s

5.Hard

A 0.2 kg ball on a string 1.4 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 = 0.2 kgr = 1.4 mv = 8 m/sg = 9.81 m/s²

T = N

6.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

Answer key

1. a_c = 0.45 m/s²
2. r_min = 555.6 m
3. v_max = 22.69 m/s
4. v_max = 20.3 m/s
5. T = 11.1 N
6. v_min = 3.431 m/s

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