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 900 kg car drives around a flat curve of radius 190 m at a constant 18 m/s. Find its centripetal acceleration a_c.

m = 900 kgv = 18 m/sr = 190 m

a_c = m/s²

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.5 m/s². What is the smallest radius r_min for a curve taken at 300 km/h?

v = 300 km/ha_max = 0.5 m/s²

r_min = m

3.Medium

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.4 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.6. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

r = 3.4 mμ_s = 0.6g = 9.81 m/s²

n = rpm

4.Medium

A road engineer wants cars to take a curve of radius 170 m at 60 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 170 mv = 60 km/hg = 9.81 m/s²

θ = °

5.Hard

A ball on a string 0.9 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 = 0.9 mg = 9.81 m/s²

v_min = m/s

6.Hard

A 0.2 kg ball on a string 0.8 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 = 0.2 kgr = 0.8 mv = 6.5 m/sg = 9.81 m/s²

T = N

Answer key

1. a_c = 1.705 m/s²
2. r_min = 13889 m
3. n = 20.94 rpm
4. θ = 9.457 °
5. v_min = 2.971 m/s
6. T = 12.52 N

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