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 1 m/s². What is the smallest radius r_min for a curve taken at 240 km/h?

v = 240 km/ha_max = 1 m/s²

r_min = m

2.Easy

A 1600 kg car drives around a flat curve of radius 100 m at a constant 17 m/s. Find the inward (centripetal) force F_c needed.

m = 1600 kgv = 17 m/sr = 100 m

F_c = N

3.Medium

A curve of radius 100 m is banked at 15°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 100 mθ = 15°g = 9.81 m/s²

v = m/s

4.Medium

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.9 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.4. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

r = 2.9 mμ_s = 0.4g = 9.81 m/s²

n = rpm

5.Hard

A ball on a string 1.1 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 = 1.1 mg = 9.81 m/s²

v_min = m/s

6.Hard

A 1.6 kg ball on a light string 1.3 m long is swung in a vertical circle. At the lowest point its speed is 11 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension T_top in the string at the highest point.

m = 1.6 kgr = 1.3 mv_bottom = 11 m/sg = 9.81 m/s²

T_top = N

Answer key

1. r_min = 4444 m
2. F_c = 4624 N
3. v = 16.21 m/s
4. n = 27.77 rpm
5. v_min = 3.285 m/s
6. T_top = 70.44 N

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