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 30 cm from the axis of a disc that turns at a steady 150 revolutions per minute. Find its centripetal acceleration a_c.

n = 150 rpmr = 0.3 m

a_c = m/s²

2.Easy

A 1400 kg car drives around a flat curve of radius 50 m at a constant 21 m/s. Find its centripetal acceleration a_c.

m = 1400 kgv = 21 m/sr = 50 m

a_c = m/s²

3.Medium

A curve of radius 210 m is banked at 18°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 210 mθ = 18°g = 9.81 m/s²

v = m/s

4.Medium

A car takes a flat curve of radius 20 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 20 mμ_s = 0.4g = 9.81 m/s²

v_max = m/s

5.Hard

A 3 kg cart is released from rest at a height of 30 m on a frictionless track and runs through a vertical loop of radius 7.5 m. Use g = 9.81 m/s². Find the normal force N_top of the track on the cart at the top of the loop.

m = 3 kgh = 30 mR = 7.5 mg = 9.81 m/s²

N_top = N

6.Hard

A curve of radius 290 m is banked at 10°, and the coefficient of static friction between tyres and road is 0.1. Use g = 9.81 m/s². Find the highest speed v_max at which a car can take the curve without sliding up and out.

r = 290 mθ = 10°μ_s = 0.1g = 9.81 m/s²

v_max = m/s

Answer key

1. a_c = 74.02 m/s²
2. a_c = 8.82 m/s²
3. v = 25.87 m/s
4. v_max = 8.859 m/s
5. N_top = 88.29 N
6. v_max = 28.29 m/s

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