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 25 cm from the axis of a disc that turns at a steady 30 revolutions per minute. Find the speed v of the object.

n = 30 rpmr = 0.25 m

v = m/s

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.8 m/s². What is the smallest radius r_min for a curve taken at 300 km/h?

v = 300 km/ha_max = 0.8 m/s²

r_min = m

3.Medium

A car takes a flat curve of radius 130 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 = 130 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 70 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 = 70 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 1.3 kg ball on a string 0.5 m long is swung in a vertical circle. At the lowest point it moves at 7 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.3 kgr = 0.5 mv = 7 m/sg = 9.81 m/s²

T = N

Answer key

1. v = 0.7854 m/s
2. r_min = 8681 m
3. v_max = 25.25 m/s
4. v_max = 16.57 m/s
5. v_min = 3.431 m/s
6. T = 140.2 N

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