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 75 cm from the axis of a disc that turns at a steady 60 revolutions per minute. Find its centripetal acceleration a_c.

n = 60 rpmr = 0.75 m

a_c = m/s²

2.Easy

A 1.1 kg stone is whirled in a horizontal circle of radius 0.8 m on a smooth, level table, held by a string that breaks at a tension of 60 N. Find the highest speed v_max the stone can have.

m = 1.1 kgr = 0.8 mT_max = 60 N

v_max = m/s

3.Medium

A small ball on a string of length 1 m moves in a horizontal circle so that the string makes a constant angle of 50° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 1 mθ = 50°g = 9.81 m/s²

T = s

4.Medium

A curve of radius 130 m is banked at 18°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 130 mθ = 18°g = 9.81 m/s²

v = m/s

5.Hard

A 0.9 kg ball on a string 1.4 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 = 1.4 mv = 8.5 m/sg = 9.81 m/s²

T = N

6.Hard

A curve of radius 190 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 highest speed v_max at which a car can take the curve without sliding up and out.

r = 190 mθ = 8°μ_s = 0.1g = 9.81 m/s²

v_max = m/s

Answer key

1. a_c = 29.61 m/s²
2. v_max = 6.606 m/s
3. T = 1.608 s
4. v = 20.36 m/s
5. T = 55.28 N
6. v_max = 21.32 m/s

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