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 = 0.85 mv150 rpm

A small object sits 85 cm from the axis of a disc that turns at a steady 150 revolutions per minute. Find its centripetal acceleration ac.

n = 150 rpmr = 0.85 m
ac = m/s²
2.Easy
r = ?240 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1 m/s². What is the smallest radius rmin for a curve taken at 240 km/h?

v = 240 km/hamax = 1 m/s²
rmin = m
3.Medium
r = 65 mvmax​ = ?

A car takes a flat curve of radius 65 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 = 65 mμs = 0.8g = 9.81 m/s²
vmax = m/s
4.Medium
L = 0.4 m50°

A small ball on a string of length 0.4 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 speed v of the ball.

L = 0.4 mθ = 50°g = 9.81 m/s²
v = m/s
5.Hard
θ = 10°to centrevmax​ = ?

A curve of radius 270 m is banked at 10°, and the coefficient of static friction between tyres and road is 0.15. 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 = 270 mθ = 10°μs = 0.15g = 9.81 m/s²
vmax = m/s
6.Hard
R = 5 mh = ?

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 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 = 5 mv₀ = 0
hmin = m

Answer key

  1. 1. ac = 209.7 m/s²
  2. 2. rmin = 4444 m
  3. 3. vmax = 22.59 m/s
  4. 4. v = 1.893 m/s
  5. 5. vmax = 29.8 m/s
  6. 6. hmin = 12.5 m

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