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 140 m at a constant 30 m/s. Find the inward (centripetal) force F_c needed.

m = 900 kgv = 30 m/sr = 140 m

F_c = N

2.Easy

A small object sits 40 cm from the axis of a disc that turns at a steady 200 revolutions per minute. Find its centripetal acceleration a_c.

n = 200 rpmr = 0.4 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 15° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 1.6 mθ = 15°g = 9.81 m/s²

v = m/s

4.Medium

A car takes a flat curve of radius 75 m. The coefficient of static friction between tyres and road is 0.5. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 75 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

5.Hard

A 0.3 kg ball on a string 1.4 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 = 0.3 kgr = 1.4 mv = 9 m/sg = 9.81 m/s²

T = N

6.Hard

A ball on a string 0.7 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 = 0.7 mg = 9.81 m/s²

v_min = m/s

Answer key

1. F_c = 5786 N
2. a_c = 175.5 m/s²
3. v = 1.043 m/s
4. v_max = 19.18 m/s
5. T = 20.3 N
6. v_min = 2.62 m/s

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