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 29 m/s. Find the inward (centripetal) force F_c needed.

m = 1600 kgv = 29 m/sr = 180 m

F_c = N

2.Easy

A small object sits 80 cm from the axis of a disc that turns at a steady 60 revolutions per minute. Find its centripetal acceleration a_c.

n = 60 rpmr = 0.8 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 30° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 1.6 mθ = 30°g = 9.81 m/s²

T = s

4.Medium

A small ball on a string of length 1.1 m moves in a horizontal circle so that the string makes a constant angle of 40° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 1.1 mθ = 40°g = 9.81 m/s²

T = s

5.Hard

A 1.9 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 = 1.9 kgr = 0.9 mv = 7 m/sg = 9.81 m/s²

T = N

6.Hard

A ball on a string 0.6 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 = 0.6 mg = 9.81 m/s²

v_min = m/s

Answer key

1. F_c = 7476 N
2. a_c = 31.58 m/s²
3. T = 2.361 s
4. T = 1.841 s
5. T = 122.1 N
6. v_min = 2.426 m/s

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