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 1500 kg car drives around a flat curve of radius 200 m at a constant 16 m/s. Find the inward (centripetal) force F_c needed.

m = 1500 kgv = 16 m/sr = 200 m

F_c = N

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.2 m/s². What is the smallest radius r_min for a curve taken at 300 km/h?

v = 300 km/ha_max = 1.2 m/s²

r_min = m

3.Medium

A car takes a flat curve of radius 45 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 = 45 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 100 m. The coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 100 mμ_s = 0.3g = 9.81 m/s²

v_max = m/s

5.Hard

A 2 kg cart is released from rest at a height of 13.2 m on a frictionless track and runs through a vertical loop of radius 3 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 = 2 kgh = 13.2 mR = 3 mg = 9.81 m/s²

N_top = N

6.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

Answer key

1. F_c = 1920 N
2. r_min = 5787 m
3. v_max = 14.86 m/s
4. v_max = 17.16 m/s
5. N_top = 74.56 N
6. v_min = 2.62 m/s

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