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 65 cm from the axis of a disc that turns at a steady 150 revolutions per minute. Find the speed v of the object.

n = 150 rpmr = 0.65 m

v = m/s

2.Easy

A 700 kg car drives around a flat curve of radius 70 m at a constant 13 m/s. Find the inward (centripetal) force F_c needed.

m = 700 kgv = 13 m/sr = 70 m

F_c = N

3.Medium

A small ball on a string of length 1.7 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 = 1.7 mθ = 20°g = 9.81 m/s²

T = s

4.Medium

A car takes a flat curve of radius 100 m. The coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 100 mμ_s = 0.3g = 9.81 m/s²

v_max = m/s

5.Hard

A 1.5 kg ball on a string 1.3 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 = 1.5 kgr = 1.3 mv = 7 m/sg = 9.81 m/s²

T = N

6.Hard

A 0.7 kg ball on a string 1 m long is swung in a vertical circle. At the lowest point it moves at 5.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.7 kgr = 1 mv = 5.5 m/sg = 9.81 m/s²

T = N

Answer key

1. v = 10.21 m/s
2. F_c = 1690 N
3. T = 2.535 s
4. v_max = 17.16 m/s
5. T = 71.25 N
6. T = 28.04 N

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