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 = 0.4 mv300 rpm

A small object sits 40 cm from the axis of a disc that turns at a steady 300 revolutions per minute. Find its centripetal acceleration ac.

n = 300 rpmr = 0.4 m
ac = m/s²
2.Easy
r = 0.55 mv90 rpm

A small object sits 55 cm from the axis of a disc that turns at a steady 90 revolutions per minute. Find its centripetal acceleration ac.

n = 90 rpmr = 0.55 m
ac = m/s²
3.Medium
r = 3.1 mn = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.1 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 = 3.1 mμs = 0.3g = 9.81 m/s²
n = rpm
4.Medium
r = 20 mvmax​ = ?

A car takes a flat curve of radius 20 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 = 20 mμs = 0.8g = 9.81 m/s²
vmax = m/s
5.Hard
R = 3 mh = 10.8 m

A 1.5 kg cart is released from rest at a height of 10.8 m on a frictionless track and runs through a vertical loop of radius 3 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 = 10.8 mR = 3 mg = 9.81 m/s²
Nbottom = N
6.Hard
r = 1.3 mv = ?

A ball on a string 1.3 m long is swung in a vertical circle. Use g = 9.81 m/s². What is the smallest speed vmin at the top for which the string just stays tight?

r = 1.3 mg = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. ac = 394.8 m/s²
  2. 2. ac = 48.85 m/s²
  3. 3. n = 31.01 rpm
  4. 4. vmax = 12.53 m/s
  5. 5. Nbottom = 120.7 N
  6. 6. vmin = 3.571 m/s

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