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 2 m/s². What is the smallest radius r_min for a curve taken at 300 km/h?

v = 300 km/ha_max = 2 m/s²

r_min = m

2.Easy

A 1700 kg car drives around a flat curve of radius 100 m at a constant 18 m/s. Find the inward (centripetal) force F_c needed.

m = 1700 kgv = 18 m/sr = 100 m

F_c = N

3.Medium

A car takes a flat curve of radius 55 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 = 55 mμ_s = 0.7g = 9.81 m/s²

v_max = m/s

4.Medium

A car drives over the top of a hump in the road, which is a circular arc of radius 40 m. Use g = 9.81 m/s². Above what speed v_max do the wheels leave the road at the top?

r = 40 mg = 9.81 m/s²

v_max = m/s

5.Hard

A ball on a string 0.7 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 = 0.7 mg = 9.81 m/s²

v_min = m/s

6.Hard

A 0.3 kg ball on a string 1.3 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 = 0.3 kgr = 1.3 mv = 6.5 m/sg = 9.81 m/s²

T = N

Answer key

1. r_min = 3472 m
2. F_c = 5508 N
3. v_max = 19.43 m/s
4. v_max = 19.81 m/s
5. v_min = 2.62 m/s
6. T = 12.69 N

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