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 40 cm from the axis of a disc that turns at a steady 120 revolutions per minute. Find the speed v of the object.

n = 120 rpmr = 0.4 m

v = m/s

2.Easy

A 1400 kg car drives around a flat curve of radius 120 m at a constant 10 m/s. Find the inward (centripetal) force F_c needed.

m = 1400 kgv = 10 m/sr = 120 m

F_c = N

3.Medium

A 1600 kg car drives over the top of a hump in the road at 24 m/s. The top of the hump is a circular arc of radius 115 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1600 kgv = 24 m/sr = 115 mg = 9.81 m/s²

N = N

4.Medium

A car takes a flat curve of radius 35 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 35 mμ_s = 0.6g = 9.81 m/s²

v_max = m/s

5.Hard

A ball on a string 1.3 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 = 1.3 mg = 9.81 m/s²

v_min = m/s

6.Hard

A 0.5 kg cart is released from rest at a height of 3.4 m on a frictionless track and runs through a vertical loop of radius 1 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 = 3.4 mR = 1 mg = 9.81 m/s²

N_top = N

Answer key

1. v = 5.027 m/s
2. F_c = 1167 N
3. N = 7682 N
4. v_max = 14.35 m/s
5. v_min = 3.571 m/s
6. N_top = 8.829 N

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