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 = 0.7 mv120 rpm

A small object sits 70 cm from the axis of a disc that turns at a steady 120 revolutions per minute. Find its centripetal acceleration ac.

n = 120 rpmr = 0.7 m
ac = m/s²
2.Easy
r = 0.95 mv200 rpm

A small object sits 95 cm from the axis of a disc that turns at a steady 200 revolutions per minute. Find its centripetal acceleration ac.

n = 200 rpmr = 0.95 m
ac = m/s²
3.Medium
r = 100 mvmax​ = ?

A car takes a flat curve of radius 100 m. The coefficient of static friction between tyres and road is 0.8. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 100 mμs = 0.8g = 9.81 m/s²
vmax = m/s
4.Medium
r = 140 mvmax​ = ?

A car takes a flat curve of radius 140 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 = 140 mμs = 0.6g = 9.81 m/s²
vmax = m/s
5.Hard
θ = 25°to centrevmin​ = ?

A curve of radius 70 m is banked at 25°, and the coefficient of static friction between tyres and road is 0.15. 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 = 70 mθ = 25°μs = 0.15g = 9.81 m/s²
vmin = m/s
6.Hard
R = 2.5 mh = ?

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 2.5 m. From what minimum height hmin above the bottom of the loop must it start to stay on the track at the top of the loop?

R = 2.5 mv₀ = 0
hmin = m

Answer key

  1. 1. ac = 110.5 m/s²
  2. 2. ac = 416.7 m/s²
  3. 3. vmax = 28.01 m/s
  4. 4. vmax = 28.71 m/s
  5. 5. vmin = 14.25 m/s
  6. 6. hmin = 6.25 m

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