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 700 kg car drives around a flat curve of radius 140 m at a constant 23 m/s. Find its centripetal acceleration a_c.

m = 700 kgv = 23 m/sr = 140 m

a_c = m/s²

2.Easy

A 1200 kg car drives around a flat curve of radius 140 m at a constant 17 m/s. Find the inward (centripetal) force F_c needed.

m = 1200 kgv = 17 m/sr = 140 m

F_c = N

3.Medium

A small ball on a string of length 1.3 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 time T for one revolution.

L = 1.3 mθ = 30°g = 9.81 m/s²

T = s

4.Medium

A car takes a flat curve of radius 110 m. The coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 110 mμ_s = 0.3g = 9.81 m/s²

v_max = m/s

5.Hard

A ball on a string 1.4 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 = 1.4 mg = 9.81 m/s²

v_min = m/s

6.Hard

A 1.3 kg ball on a string 0.6 m long is swung in a vertical circle. At the lowest point it moves at 5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.3 kgr = 0.6 mv = 5 m/sg = 9.81 m/s²

T = N

Answer key

1. a_c = 3.779 m/s²
2. F_c = 2477 N
3. T = 2.129 s
4. v_max = 17.99 m/s
5. v_min = 3.706 m/s
6. T = 66.92 N

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