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 = 1.5 mv = ?78 rpm

A small object sits 150 cm from the axis of a disc that turns at a steady 78 revolutions per minute. Find the speed v of the object.

n = 78 rpmr = 1.5 m
v = m/s
2.Easy
r = 1.8 mvmax​ = ?

A 0.2 kg stone is whirled in a horizontal circle of radius 1.8 m on a smooth, level table, held by a string that breaks at a tension of 180 N. Find the highest speed vmax the stone can have.

m = 0.2 kgr = 1.8 mTmax = 180 N
vmax = m/s
3.Medium
r = 40 mvmax​ = ?

A car takes a flat curve of radius 40 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 40 mμs = 0.4g = 9.81 m/s²
vmax = m/s
4.Medium
L = 0.4 m30°

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 30° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 0.4 mθ = 30°g = 9.81 m/s²
T = s
5.Hard
r = 0.5 mv = ?

A ball on a string 0.5 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 = 0.5 mg = 9.81 m/s²
vmin = m/s
6.Hard
R = 1 mh = 4.9 m

A 0.5 kg cart is released from rest at a height of 4.9 m on a frictionless track and runs through a vertical loop of radius 1 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 = 0.5 kgh = 4.9 mR = 1 mg = 9.81 m/s²
Nbottom = N

Answer key

  1. 1. v = 12.25 m/s
  2. 2. vmax = 40.25 m/s
  3. 3. vmax = 12.53 m/s
  4. 4. T = 1.181 s
  5. 5. vmin = 2.215 m/s
  6. 6. Nbottom = 52.97 N

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