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 120 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 = 1.2 m

v = m/s

2.Easy

A 0.5 kg stone is whirled in a horizontal circle of radius 0.9 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 = 0.5 kgr = 0.9 mT_max = 90 N

v_max = m/s

3.Medium

A road engineer wants cars to take a curve of radius 210 m at 90 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 210 mv = 90 km/hg = 9.81 m/s²

θ = °

4.Medium

A small ball on a string of length 1.5 m moves in a horizontal circle so that the string makes a constant angle of 40° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 1.5 mθ = 40°g = 9.81 m/s²

T = s

5.Hard

A 0.2 kg ball on a string 1.5 m long is swung in a vertical circle. At the lowest point it moves at 3 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.2 kgr = 1.5 mv = 3 m/sg = 9.81 m/s²

T = N

6.Hard

A 1.3 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 = 1.3 kgr = 0.8 mv = 6 m/sg = 9.81 m/s²

T = N

Answer key

1. v = 3.77 m/s
2. v_max = 12.73 m/s
3. θ = 16.88 °
4. T = 2.15 s
5. T = 3.162 N
6. T = 71.25 N

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