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 1400 kg car drives around a flat curve of radius 50 m at a constant 16 m/s. Find its centripetal acceleration a_c.

m = 1400 kgv = 16 m/sr = 50 m

a_c = m/s²

2.Easy

A 1700 kg car drives around a flat curve of radius 90 m at a constant 8 m/s. Find the inward (centripetal) force F_c needed.

m = 1700 kgv = 8 m/sr = 90 m

F_c = N

3.Medium

A small ball on a string of length 1.6 m moves in a horizontal circle so that the string makes a constant angle of 30° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 1.6 mθ = 30°g = 9.81 m/s²

v = m/s

4.Medium

A car drives over the top of a hump in the road, which is a circular arc of radius 80 m. Use g = 9.81 m/s². Above what speed v_max do the wheels leave the road at the top?

r = 80 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 8.5 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 = 8.5 mv₀ = 0

h_min = m

6.Hard

A ball on a string 1.2 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 = 1.2 mg = 9.81 m/s²

v_min = m/s

Answer key

1. a_c = 5.12 m/s²
2. F_c = 1209 N
3. v = 2.129 m/s
4. v_max = 28.01 m/s
5. h_min = 21.25 m
6. v_min = 3.431 m/s

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