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 1600 kg car drives around a flat curve of radius 180 m at a constant 9 m/s. Find the inward (centripetal) force F_c needed.

m = 1600 kgv = 9 m/sr = 180 m

F_c = N

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.5 m/s². What is the smallest radius r_min for a curve taken at 240 km/h?

v = 240 km/ha_max = 1.5 m/s²

r_min = m

3.Medium

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.6 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.8. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.

r = 2.6 mμ_s = 0.8g = 9.81 m/s²

ω = rad/s

4.Medium

A curve of radius 320 m is banked at 18°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 320 mθ = 18°g = 9.81 m/s²

v = m/s

5.Hard

A 1.6 kg ball on a light string 0.6 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 = 0.6 mv_bottom = 11 m/sg = 9.81 m/s²

T_top = N

6.Hard

A 0.4 kg ball on a string 0.9 m long is swung in a vertical circle. At the lowest point it moves at 7 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.4 kgr = 0.9 mv = 7 m/sg = 9.81 m/s²

T = N

Answer key

1. F_c = 720 N
2. r_min = 2963 m
3. ω = 2.172 rad/s
4. v = 31.94 m/s
5. T_top = 244.2 N
6. T = 25.7 N

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