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 = 0.15 mv = ?150 rpm

A small object sits 15 cm from the axis of a disc that turns at a steady 150 revolutions per minute. Find the speed v of the object.

n = 150 rpmr = 0.15 m
v = m/s
2.Easy
r = 70 m23 m/sac​ = ?

A 600 kg car drives around a flat curve of radius 70 m at a constant 23 m/s. Find its centripetal acceleration ac.

m = 600 kgv = 23 m/sr = 70 m
ac = m/s²
3.Medium
r = 3.5 mn = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.5 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 = 3.5 mμs = 0.3g = 9.81 m/s²
n = rpm
4.Medium
r = 50 mvmax​ = ?

A car takes a flat curve of radius 50 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 = 50 mμs = 0.8g = 9.81 m/s²
vmax = m/s
5.Hard
θ = 8°to centrevmax​ = ?

A curve of radius 50 m is banked at 8°, 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 = 50 mθ = 8°μs = 0.15g = 9.81 m/s²
vmax = m/s
6.Hard
R = 9.5 mh = 40.85 m

A 1.5 kg cart is released from rest at a height of 40.85 m on a frictionless track and runs through a vertical loop of radius 9.5 m. Use g = 9.81 m/s². Find the normal force Nbottom of the track on the cart at the bottom of the loop.

m = 1.5 kgh = 40.85 mR = 9.5 mg = 9.81 m/s²
Nbottom = N

Answer key

  1. 1. v = 2.356 m/s
  2. 2. ac = 7.557 m/s²
  3. 3. n = 29.19 rpm
  4. 4. vmax = 19.81 m/s
  5. 5. vmax = 12.07 m/s
  6. 6. Nbottom = 141.3 N

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