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

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.2 m/s². What is the smallest radius r_min for a curve taken at 160 km/h?

v = 160 km/ha_max = 1.2 m/s²

r_min = m

2.Easy

A small object sits 60 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 = 0.6 m

a_c = m/s²

3.Medium

A road engineer wants cars to take a curve of radius 120 m at 90 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 120 mv = 90 km/hg = 9.81 m/s²

θ = °

4.Medium

A car takes a flat curve of radius 30 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 = 30 mμ_s = 0.8g = 9.81 m/s²

v_max = m/s

5.Hard

A 1.4 kg ball on a string 0.8 m long is swung in a vertical circle. At the lowest point it moves at 6 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.4 kgr = 0.8 mv = 6 m/sg = 9.81 m/s²

T = N

6.Hard

A 1.8 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 = 1.8 kgr = 0.9 mv = 3.5 m/sg = 9.81 m/s²

T = N

Answer key

1. r_min = 1646 m
2. a_c = 148 m/s²
3. θ = 27.96 °
4. v_max = 15.34 m/s
5. T = 76.73 N
6. T = 42.16 N

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