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 1500 kg car drives around a flat curve of radius 80 m at a constant 24 m/s. Find its centripetal acceleration a_c.

m = 1500 kgv = 24 m/sr = 80 m

a_c = m/s²

2.Easy

A 1500 kg car drives around a flat curve of radius 100 m at a constant 9 m/s. Find its centripetal acceleration a_c.

m = 1500 kgv = 9 m/sr = 100 m

a_c = m/s²

3.Medium

A small ball on a string of length 1.6 m moves in a horizontal circle so that the string makes a constant angle of 20° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 1.6 mθ = 20°g = 9.81 m/s²

T = s

4.Medium

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.7 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 = 2.7 mμ_s = 0.4g = 9.81 m/s²

n = rpm

5.Hard

A 1.2 kg ball on a string 1.3 m long is swung in a vertical circle. At the lowest point it moves at 5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.2 kgr = 1.3 mv = 5 m/sg = 9.81 m/s²

T = N

6.Hard

A 0.5 kg ball on a string 0.7 m long is swung in a vertical circle. At the lowest point it moves at 9 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.5 kgr = 0.7 mv = 9 m/sg = 9.81 m/s²

T = N

Answer key

1. a_c = 7.2 m/s²
2. a_c = 0.81 m/s²
3. T = 2.46 s
4. n = 28.78 rpm
5. T = 34.85 N
6. T = 62.76 N

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