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

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.8 m/s². What is the smallest radius r_min for a curve taken at 160 km/h?

v = 160 km/ha_max = 0.8 m/s²

r_min = m

2.Easy

A 700 kg car drives around a flat curve of radius 200 m at a constant 13 m/s. Find the inward (centripetal) force F_c needed.

m = 700 kgv = 13 m/sr = 200 m

F_c = N

3.Medium

A car takes a flat curve of radius 105 m. The coefficient of static friction between tyres and road is 0.8. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 105 mμ_s = 0.8g = 9.81 m/s²

v_max = m/s

4.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

5.Hard

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 8 m. From what minimum height h_min above the bottom of the loop must it start to stay on the track at the top of the loop?

R = 8 mv₀ = 0

h_min = m

6.Hard

A 1 kg ball on a string 1.4 m long is swung in a vertical circle. At the lowest point it moves at 6.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1 kgr = 1.4 mv = 6.5 m/sg = 9.81 m/s²

T = N

Answer key

1. r_min = 2469 m
2. F_c = 591.5 N
3. v_max = 28.71 m/s
4. v_max = 23.23 m/s
5. h_min = 20 m
6. T = 39.99 N

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