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 1100 kg car drives around a flat curve of radius 60 m at a constant 27 m/s. Find the inward (centripetal) force F_c needed.

m = 1100 kgv = 27 m/sr = 60 m

F_c = N

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.2 m/s². What is the smallest radius r_min for a curve taken at 300 km/h?

v = 300 km/ha_max = 1.2 m/s²

r_min = m

3.Medium

A curve of radius 60 m is banked at 20°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 60 mθ = 20°g = 9.81 m/s²

v = m/s

4.Medium

A car takes a flat curve of radius 55 m. The coefficient of static friction between tyres and road is 0.8. 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 = 0.8g = 9.81 m/s²

v_max = m/s

5.Hard

A 0.2 kg ball on a string 1.3 m long is swung in a vertical circle. At the lowest point it moves at 4 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.2 kgr = 1.3 mv = 4 m/sg = 9.81 m/s²

T = N

6.Hard

A 1.3 kg ball on a string 0.6 m long is swung in a vertical circle. At the lowest point it moves at 4.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.3 kgr = 0.6 mv = 4.5 m/sg = 9.81 m/s²

T = N

Answer key

1. F_c = 13365 N
2. r_min = 5787 m
3. v = 14.64 m/s
4. v_max = 20.78 m/s
5. T = 4.424 N
6. T = 56.63 N

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