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 small object sits 145 cm from the axis of a disc that turns at a steady 45 revolutions per minute. Find the speed v of the object.

n = 45 rpmr = 1.45 m

v = m/s

2.Easy

A 1100 kg car drives around a flat curve of radius 110 m at a constant 26 m/s. Find its centripetal acceleration a_c.

m = 1100 kgv = 26 m/sr = 110 m

a_c = m/s²

3.Medium

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.2 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 = 3.2 mμ_s = 0.4g = 9.81 m/s²

n = rpm

4.Medium

A curve of radius 190 m is banked at 12°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 190 mθ = 12°g = 9.81 m/s²

v = m/s

5.Hard

A 2 kg ball on a string 1.4 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 = 2 kgr = 1.4 mv = 4.5 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 7.5 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 = 7.5 m/sg = 9.81 m/s²

T = N

Answer key

1. v = 6.833 m/s
2. a_c = 6.145 m/s²
3. n = 26.44 rpm
4. v = 19.9 m/s
5. T = 48.55 N
6. T = 134.6 N

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