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 1300 kg car drives around a flat curve of radius 190 m at a constant 20 m/s. Find the inward (centripetal) force F_c needed.

m = 1300 kgv = 20 m/sr = 190 m

F_c = N

2.Easy

A 1100 kg car drives around a flat curve of radius 180 m at a constant 25 m/s. Find its centripetal acceleration a_c.

m = 1100 kgv = 25 m/sr = 180 m

a_c = m/s²

3.Medium

A car drives over the top of a hump in the road, which is a circular arc of radius 20 m. Use g = 9.81 m/s². Above what speed v_max do the wheels leave the road at the top?

r = 20 mg = 9.81 m/s²

v_max = m/s

4.Medium

A curve of radius 80 m is banked at 5°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 80 mθ = 5°g = 9.81 m/s²

v = m/s

5.Hard

A 2 kg cart is released from rest at a height of 16.8 m on a frictionless track and runs through a vertical loop of radius 4 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 = 16.8 mR = 4 mg = 9.81 m/s²

N_top = N

6.Hard

A 1.4 kg ball on a light string 0.5 m long is swung in a vertical circle. At the lowest point its speed is 7 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension T_top in the string at the highest point.

m = 1.4 kgr = 0.5 mv_bottom = 7 m/sg = 9.81 m/s²

T_top = N

Answer key

1. F_c = 2737 N
2. a_c = 3.472 m/s²
3. v_max = 14.01 m/s
4. v = 8.286 m/s
5. N_top = 66.71 N
6. T_top = 68.53 N

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