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 1.9 kg stone is whirled in a horizontal circle of radius 1.4 m on a smooth, level table, held by a string that breaks at a tension of 90 N. Find the highest speed v_max the stone can have.

m = 1.9 kgr = 1.4 mT_max = 90 N

v_max = m/s

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 2 m/s². What is the smallest radius r_min for a curve taken at 250 km/h?

v = 250 km/ha_max = 2 m/s²

r_min = m

3.Medium

A road engineer wants cars to take a curve of radius 200 m at 100 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 200 mv = 100 km/hg = 9.81 m/s²

θ = °

4.Medium

A small ball on a string of length 2 m moves in a horizontal circle so that the string makes a constant angle of 20° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 2 mθ = 20°g = 9.81 m/s²

v = m/s

5.Hard

A 0.9 kg ball on a string 0.5 m long is swung in a vertical circle. At the lowest point it moves at 5.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.9 kgr = 0.5 mv = 5.5 m/sg = 9.81 m/s²

T = N

6.Hard

A 0.9 kg ball on a string 0.7 m long is swung in a vertical circle. At the lowest point it moves at 8.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.9 kgr = 0.7 mv = 8.5 m/sg = 9.81 m/s²

T = N

Answer key

1. v_max = 8.143 m/s
2. r_min = 2411 m
3. θ = 21.47 °
4. v = 1.563 m/s
5. T = 63.28 N
6. T = 101.7 N

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