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 1600 kg car drives around a flat curve of radius 50 m at a constant 30 m/s. Find the inward (centripetal) force F_c needed.

m = 1600 kgv = 30 m/sr = 50 m

F_c = N

2.Easy

A 1500 kg car drives around a flat curve of radius 140 m at a constant 28 m/s. Find the inward (centripetal) force F_c needed.

m = 1500 kgv = 28 m/sr = 140 m

F_c = N

3.Medium

A small ball on a string of length 1.1 m moves in a horizontal circle so that the string makes a constant angle of 60° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 1.1 mθ = 60°g = 9.81 m/s²

T = s

4.Medium

A car takes a flat curve of radius 75 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 75 mμ_s = 0.6g = 9.81 m/s²

v_max = m/s

5.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

6.Hard

A 4.5 kg cart is released from rest at a height of 39.1 m on a frictionless track and runs through a vertical loop of radius 8.5 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 = 4.5 kgh = 39.1 mR = 8.5 mg = 9.81 m/s²

N_top = N

Answer key

1. F_c = 28800 N
2. F_c = 8400 N
3. T = 1.488 s
4. v_max = 21.01 m/s
5. v_min = 2.62 m/s
6. N_top = 185.4 N

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