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 40 cm from the axis of a disc that turns at a steady 33 revolutions per minute. Find its centripetal acceleration a_c.

n = 33 rpmr = 0.4 m

a_c = m/s²

2.Easy

A small object sits 15 cm from the axis of a disc that turns at a steady 150 revolutions per minute. Find its centripetal acceleration a_c.

n = 150 rpmr = 0.15 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 90 m. The coefficient of static friction between tyres and road is 0.8. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 90 mμ_s = 0.8g = 9.81 m/s²

v_max = m/s

4.Medium

A curve of radius 140 m is banked at 18°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 140 mθ = 18°g = 9.81 m/s²

v = m/s

5.Hard

A 1.4 kg ball on a string 0.7 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 = 1.4 kgr = 0.7 mv = 7.5 m/sg = 9.81 m/s²

T = N

6.Hard

A curve of radius 50 m is banked at 12°, and 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 a car can take the curve without sliding up and out.

r = 50 mθ = 12°μ_s = 0.4g = 9.81 m/s²

v_max = m/s

Answer key

1. a_c = 4.777 m/s²
2. a_c = 37.01 m/s²
3. v_max = 26.58 m/s
4. v = 21.12 m/s
5. T = 126.2 N
6. v_max = 18.12 m/s

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