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 = 0.25 mv120 rpm

A small object sits 25 cm from the axis of a disc that turns at a steady 120 revolutions per minute. Find its centripetal acceleration ac.

n = 120 rpmr = 0.25 m
ac = m/s²
2.Easy
r = ?120 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.8 m/s². What is the smallest radius rmin for a curve taken at 120 km/h?

v = 120 km/hamax = 0.8 m/s²
rmin = m
3.Medium
r = 40 mvmax​ = ?

A car takes a flat curve of radius 40 m. 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 the car can take the curve without skidding.

r = 40 mμs = 0.4g = 9.81 m/s²
vmax = m/s
4.Medium
r = 135 mvmax​ = ?

A car takes a flat curve of radius 135 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 135 mμs = 0.6g = 9.81 m/s²
vmax = m/s
5.Hard
R = 7.5 mh = 29.25 m

A 4 kg cart is released from rest at a height of 29.25 m on a frictionless track and runs through a vertical loop of radius 7.5 m. Use g = 9.81 m/s². Find the normal force Ntop of the track on the cart at the top of the loop.

m = 4 kgh = 29.25 mR = 7.5 mg = 9.81 m/s²
Ntop = N
6.Hard
θ = 10°to centrevmin​ = ?

A curve of radius 190 m is banked at 10°, 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 = 190 mθ = 10°μs = 0.1g = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. ac = 39.48 m/s²
  2. 2. rmin = 1389 m
  3. 3. vmax = 12.53 m/s
  4. 4. vmax = 28.19 m/s
  5. 5. Ntop = 109.9 N
  6. 6. vmin = 11.82 m/s

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