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 = 1.2 mv33 rpm

A small object sits 120 cm from the axis of a disc that turns at a steady 33 revolutions per minute. Find its centripetal acceleration ac.

n = 33 rpmr = 1.2 m
ac = m/s²
2.Easy
r = ?240 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.2 m/s². What is the smallest radius rmin for a curve taken at 240 km/h?

v = 240 km/hamax = 1.2 m/s²
rmin = m
3.Medium
r = 3.7 mn = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.7 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 = 3.7 mμs = 0.3g = 9.81 m/s²
n = rpm
4.Medium
r = 1.8 mω = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 1.8 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 angular speed ω in rad/s.

r = 1.8 mμs = 0.3g = 9.81 m/s²
ω = rad/s
5.Hard
θ = 18°to centrevmin​ = ?

A curve of radius 170 m is banked at 18°, 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 = 170 mθ = 18°μs = 0.1g = 9.81 m/s²
vmin = m/s
6.Hard
R = 7 mh = 30.8 m

A 5 kg cart is released from rest at a height of 30.8 m on a frictionless track and runs through a vertical loop of radius 7 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 = 5 kgh = 30.8 mR = 7 mg = 9.81 m/s²
Nbottom = N

Answer key

  1. 1. ac = 14.33 m/s²
  2. 2. rmin = 3704 m
  3. 3. n = 28.39 rpm
  4. 4. ω = 4.262 rad/s
  5. 5. vmin = 19.06 m/s
  6. 6. Nbottom = 480.7 N

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