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 mv90 rpm

A small object sits 45 cm from the axis of a disc that turns at a steady 90 revolutions per minute. Find its centripetal acceleration ac.

n = 90 rpmr = 0.45 m
ac = m/s²
2.Easy
r = 110 m28 m/sF = ?

A 600 kg car drives around a flat curve of radius 110 m at a constant 28 m/s. Find the inward (centripetal) force Fc needed.

m = 600 kgv = 28 m/sr = 110 m
Fc = N
3.Medium
L = 0.4 m20°

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 20° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 0.4 mθ = 20°g = 9.81 m/s²
T = s
4.Medium
r = 75 mvmax​ = ?

A car takes a flat curve of radius 75 m. The coefficient of static friction between tyres and road is 0.5. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 75 mμs = 0.5g = 9.81 m/s²
vmax = m/s
5.Hard
θ = 30°to centrevmax​ = ?

A curve of radius 290 m is banked at 30°, 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 = 290 mθ = 30°μs = 0.25g = 9.81 m/s²
vmax = m/s
6.Hard
R = 1.5 mh = ?

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 1.5 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 = 1.5 mv₀ = 0
hmin = m

Answer key

  1. 1. ac = 39.97 m/s²
  2. 2. Fc = 4276 N
  3. 3. T = 1.23 s
  4. 4. vmax = 19.18 m/s
  5. 5. vmax = 52.45 m/s
  6. 6. hmin = 3.75 m

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