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 150 m at a constant 9 m/s. Find the inward (centripetal) force F_c needed.

m = 600 kgv = 9 m/sr = 150 m

F_c = N

2.Easy

An 800 kg car drives around a flat curve of radius 120 m at a constant 12 m/s. Find its centripetal acceleration a_c.

m = 800 kgv = 12 m/sr = 120 m

a_c = m/s²

3.Medium

A small ball on a string of length 0.4 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 = 0.4 mθ = 15°g = 9.81 m/s²

v = m/s

4.Medium

A car takes a flat curve of radius 40 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 40 mμ_s = 0.4g = 9.81 m/s²

v_max = m/s

5.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

6.Hard

A 0.5 kg ball on a string 0.9 m long is swung in a vertical circle. At the lowest point it moves at 3.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.5 kgr = 0.9 mv = 3.5 m/sg = 9.81 m/s²

T = N

Answer key

1. F_c = 324 N
2. a_c = 1.2 m/s²
3. v = 0.5217 m/s
4. v_max = 12.53 m/s
5. v_min = 3.431 m/s
6. T = 11.71 N

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