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 700 kg car drives around a flat curve of radius 20 m at a constant 23 m/s. Find the inward (centripetal) force F_c needed.

m = 700 kgv = 23 m/sr = 20 m

F_c = N

2.Easy

A 1800 kg car drives around a flat curve of radius 40 m at a constant 20 m/s. Find the inward (centripetal) force F_c needed.

m = 1800 kgv = 20 m/sr = 40 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 50 m. Use g = 9.81 m/s². Above what speed v_max do the wheels leave the road at the top?

r = 50 mg = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 80 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 = 80 mμ_s = 0.3g = 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 3.5 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 = 3.5 mv₀ = 0

h_min = m

6.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

Answer key

1. F_c = 18515 N
2. F_c = 18000 N
3. v_max = 22.15 m/s
4. v_max = 15.34 m/s
5. h_min = 8.75 m
6. v_min = 3.571 m/s

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