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
r = 0.45 mv33 rpm

A small object sits 45 cm from the axis of a disc that turns at a steady 33 revolutions per minute. Find its centripetal acceleration ac.

n = 33 rpmr = 0.45 m
ac = m/s²
2.Easy
r = 0.9 mvmax​ = ?

A 0.8 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 110 N. Find the highest speed vmax the stone can have.

m = 0.8 kgr = 0.9 mTmax = 110 N
vmax = m/s
3.Medium
r = 110 m22 m/s

A 900 kg car drives over the top of a hump in the road at 22 m/s. The top of the hump is a circular arc of radius 110 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 900 kgv = 22 m/sr = 110 mg = 9.81 m/s²
N = N
4.Medium
L = 1.5 m35°

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 35° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 1.5 mθ = 35°g = 9.81 m/s²
T = s
5.Hard
θ = 18°to centrevmax​ = ?

A curve of radius 120 m is banked at 18°, and the coefficient of static friction between tyres and road is 0.25. Use g = 9.81 m/s². Find the highest speed vmax at which a car can take the curve without sliding up and out.

r = 120 mθ = 18°μs = 0.25g = 9.81 m/s²
vmax = m/s
6.Hard
θ = 20°to centrevmin​ = ?

A curve of radius 200 m is banked at 20°, and the coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the lowest speed vmin at which a car can take the curve without sliding down the bank.

r = 200 mθ = 20°μs = 0.3g = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. ac = 5.374 m/s²
  2. 2. vmax = 11.12 m/s
  3. 3. N = 4869 N
  4. 4. T = 2.224 s
  5. 5. vmax = 27.14 m/s
  6. 6. vmin = 10.64 m/s

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