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 small object sits 95 cm from the axis of a disc that turns at a steady 300 revolutions per minute. Find the speed v of the object.

n = 300 rpmr = 0.95 m

v = m/s

2.Easy

A 900 kg car drives around a flat curve of radius 60 m at a constant 14 m/s. Find its centripetal acceleration a_c.

m = 900 kgv = 14 m/sr = 60 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 35 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 = 35 mμ_s = 0.4g = 9.81 m/s²

v_max = m/s

4.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 45° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 1.1 mθ = 45°g = 9.81 m/s²

T = s

5.Hard

A curve of radius 60 m is banked at 25°, and 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 a car can take the curve without sliding up and out.

r = 60 mθ = 25°μ_s = 0.3g = 9.81 m/s²

v_max = m/s

6.Hard

A 1.1 kg ball on a string 0.6 m long is swung in a vertical circle. At the lowest point it moves at 7.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.1 kgr = 0.6 mv = 7.5 m/sg = 9.81 m/s²

T = N

Answer key

1. v = 29.85 m/s
2. a_c = 3.267 m/s²
3. v_max = 11.72 m/s
4. T = 1.769 s
5. v_max = 22.9 m/s
6. T = 113.9 N

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