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 = 0.05 mv30 rpm

A small object sits 5 cm from the axis of a disc that turns at a steady 30 revolutions per minute. Find its centripetal acceleration ac.

n = 30 rpmr = 0.05 m
ac = m/s²
2.Easy
r = ?300 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 2 m/s². What is the smallest radius rmin for a curve taken at 300 km/h?

v = 300 km/hamax = 2 m/s²
rmin = m
3.Medium
L = 0.5 m45°

A small ball on a string of length 0.5 m moves in a horizontal circle so that the string makes a constant angle of 45° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 0.5 mθ = 45°g = 9.81 m/s²
T = s
4.Medium
r = 2 mn = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.3. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

r = 2 mμs = 0.3g = 9.81 m/s²
n = rpm
5.Hard
θ = 15°to centrevmin​ = ?

A curve of radius 290 m is banked at 15°, and the coefficient of static friction between tyres and road is 0.1. 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 = 290 mθ = 15°μs = 0.1g = 9.81 m/s²
vmin = m/s
6.Hard
θ = 30°to centrevmax​ = ?

A curve of radius 250 m is banked at 30°, and the coefficient of static friction between tyres and road is 0.4. 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 = 250 mθ = 30°μs = 0.4g = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. ac = 0.4935 m/s²
  2. 2. rmin = 3472 m
  3. 3. T = 1.193 s
  4. 4. n = 38.61 rpm
  5. 5. vmin = 21.57 m/s
  6. 6. vmax = 55.83 m/s

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