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 0.8 m/s². What is the smallest radius r_min for a curve taken at 200 km/h?

v = 200 km/ha_max = 0.8 m/s²

r_min = m

2.Easy

A 1000 kg car drives around a flat curve of radius 70 m at a constant 10 m/s. Find its centripetal acceleration a_c.

m = 1000 kgv = 10 m/sr = 70 m

a_c = m/s²

3.Medium

A road engineer wants cars to take a curve of radius 130 m at 60 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 130 mv = 60 km/hg = 9.81 m/s²

θ = °

4.Medium

A car takes a flat curve of radius 25 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 = 25 mμ_s = 0.8g = 9.81 m/s²

v_max = m/s

5.Hard

A 0.3 kg ball on a light string 0.9 m long is swung in a vertical circle. At the lowest point its speed is 12 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension T_top in the string at the highest point.

m = 0.3 kgr = 0.9 mv_bottom = 12 m/sg = 9.81 m/s²

T_top = N

6.Hard

A 1 kg ball on a string 1.2 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 kgr = 1.2 mv = 7.5 m/sg = 9.81 m/s²

T = N

Answer key

1. r_min = 3858 m
2. a_c = 1.429 m/s²
3. θ = 12.29 °
4. v_max = 14.01 m/s
5. T_top = 33.28 N
6. T = 56.69 N

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