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 600 kg car drives around a flat curve of radius 80 m at a constant 17 m/s. Find the inward (centripetal) force F_c needed.

m = 600 kgv = 17 m/sr = 80 m

F_c = N

2.Easy

A 600 kg car drives around a flat curve of radius 140 m at a constant 14 m/s. Find the inward (centripetal) force F_c needed.

m = 600 kgv = 14 m/sr = 140 m

F_c = N

3.Medium

A car takes a flat curve of radius 120 m. The coefficient of static friction between tyres and road is 0.5. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 120 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

4.Medium

A small ball on a string of length 1.8 m moves in a horizontal circle so that the string makes a constant angle of 15° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 1.8 mθ = 15°g = 9.81 m/s²

v = m/s

5.Hard

A 1.9 kg ball on a string 1.5 m long is swung in a vertical circle. At the lowest point it moves at 8 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.9 kgr = 1.5 mv = 8 m/sg = 9.81 m/s²

T = N

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. F_c = 2168 N
2. F_c = 840 N
3. v_max = 24.26 m/s
4. v = 1.107 m/s
5. T = 99.71 N
6. v_min = 3.431 m/s

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