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 60 cm from the axis of a disc that turns at a steady 33 revolutions per minute. Find its centripetal acceleration a_c.

n = 33 rpmr = 0.6 m

a_c = m/s²

2.Easy

A 1800 kg car drives around a flat curve of radius 200 m at a constant 9 m/s. Find its centripetal acceleration a_c.

m = 1800 kgv = 9 m/sr = 200 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 85 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 = 85 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

4.Medium

A small ball on a string of length 1.2 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 = 1.2 mθ = 30°g = 9.81 m/s²

T = s

5.Hard

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 2 m. From what minimum height h_min above the bottom of the loop must it start to stay on the track at the top of the loop?

R = 2 mv₀ = 0

h_min = m

6.Hard

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 5.5 m. From what minimum height h_min above the bottom of the loop must it start to stay on the track at the top of the loop?

R = 5.5 mv₀ = 0

h_min = m

Answer key

1. a_c = 7.165 m/s²
2. a_c = 0.405 m/s²
3. v_max = 20.42 m/s
4. T = 2.045 s
5. h_min = 5 m
6. h_min = 13.75 m

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