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

An 800 kg car drives around a flat curve of radius 50 m at a constant 22 m/s. Find the inward (centripetal) force F_c needed.

m = 800 kgv = 22 m/sr = 50 m

F_c = N

2.Easy

A small object sits 145 cm from the axis of a disc that turns at a steady 30 revolutions per minute. Find the speed v of the object.

n = 30 rpmr = 1.45 m

v = m/s

3.Medium

A car takes a flat curve of radius 85 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 = 85 mμ_s = 0.6g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 65 m. The coefficient of static friction between tyres and road is 0.7. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 65 mμ_s = 0.7g = 9.81 m/s²

v_max = m/s

5.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

6.Hard

A 4.5 kg cart is released from rest at a height of 25.2 m on a frictionless track and runs through a vertical loop of radius 7 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 = 4.5 kgh = 25.2 mR = 7 mg = 9.81 m/s²

N_top = N

Answer key

1. F_c = 7744 N
2. v = 4.555 m/s
3. v_max = 22.37 m/s
4. v_max = 21.13 m/s
5. v_min = 2.62 m/s
6. N_top = 97.12 N

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