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 900 kg car drives around a flat curve of radius 140 m at a constant 10 m/s. Find its centripetal acceleration a_c.

m = 900 kgv = 10 m/sr = 140 m

a_c = m/s²

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.5 m/s². What is the smallest radius r_min for a curve taken at 120 km/h?

v = 120 km/ha_max = 0.5 m/s²

r_min = m

3.Medium

A car takes a flat curve of radius 60 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 = 60 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

4.Medium

A road engineer wants cars to take a curve of radius 110 m at 100 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 110 mv = 100 km/hg = 9.81 m/s²

θ = °

5.Hard

A 1 kg ball on a string 0.7 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 kgr = 0.7 mv = 5 m/sg = 9.81 m/s²

T = N

6.Hard

A curve of radius 110 m is banked at 8°, and the coefficient of static friction between tyres and road is 0.1. Use g = 9.81 m/s². Find the lowest speed v_min at which a car can take the curve without sliding down the bank.

r = 110 mθ = 8°μ_s = 0.1g = 9.81 m/s²

v_min = m/s

Answer key

1. a_c = 0.7143 m/s²
2. r_min = 2222 m
3. v_max = 17.16 m/s
4. θ = 35.57 °
5. T = 45.52 N
6. v_min = 6.568 m/s

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