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 115 cm from the axis of a disc that turns at a steady 78 revolutions per minute. Find its centripetal acceleration a_c.

n = 78 rpmr = 1.15 m

a_c = m/s²

2.Easy

A 700 kg car drives around a flat curve of radius 110 m at a constant 9 m/s. Find its centripetal acceleration a_c.

m = 700 kgv = 9 m/sr = 110 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 110 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 = 110 mμ_s = 0.4g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 145 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 = 145 mμ_s = 0.5g = 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 3 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 = 3 m/sg = 9.81 m/s²

T = N

6.Hard

A 0.5 kg cart is released from rest at a height of 8.5 m on a frictionless track and runs through a vertical loop of radius 2.5 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 = 0.5 kgh = 8.5 mR = 2.5 mg = 9.81 m/s²

N_top = N

Answer key

1. a_c = 76.73 m/s²
2. a_c = 0.7364 m/s²
3. v_max = 20.78 m/s
4. v_max = 26.67 m/s
5. T = 25.1 N
6. N_top = 8.829 N

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