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 5 cm from the axis of a disc that turns at a steady 300 revolutions per minute. Find its centripetal acceleration a_c.

n = 300 rpmr = 0.05 m

a_c = m/s²

2.Easy

A 600 kg car drives around a flat curve of radius 90 m at a constant 24 m/s. Find the inward (centripetal) force F_c needed.

m = 600 kgv = 24 m/sr = 90 m

F_c = N

3.Medium

A car drives over the top of a hump in the road, which is a circular arc of radius 55 m. Use g = 9.81 m/s². Above what speed v_max do the wheels leave the road at the top?

r = 55 mg = 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 0.6. 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 = 0.6g = 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 25.5 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_bottom of the track on the cart at the bottom of the loop.

m = 0.5 kgh = 25.5 mR = 7.5 mg = 9.81 m/s²

N_bottom = N

Answer key

1. a_c = 49.35 m/s²
2. F_c = 3840 N
3. v_max = 23.23 m/s
4. v_max = 29.21 m/s
5. v_min = 3.571 m/s
6. N_bottom = 38.26 N

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