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 = 0.5 mv = ?33 rpm

A small object sits 50 cm from the axis of a disc that turns at a steady 33 revolutions per minute. Find the speed v of the object.

n = 33 rpmr = 0.5 m
v = m/s
2.Easy
r = 0.9 mvmax​ = ?

A 1.7 kg stone is whirled in a horizontal circle of radius 0.9 m on a smooth, level table, held by a string that breaks at a tension of 140 N. Find the highest speed vmax the stone can have.

m = 1.7 kgr = 0.9 mTmax = 140 N
vmax = m/s
3.Medium
r = 35 mvmax​ = ?

A car takes a flat curve of radius 35 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 = 35 mμs = 0.5g = 9.81 m/s²
vmax = m/s
4.Medium
r = 4 mω = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 4 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.8. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.

r = 4 mμs = 0.8g = 9.81 m/s²
ω = rad/s
5.Hard
r = 0.6 mv = ?

A ball on a string 0.6 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 = 0.6 mg = 9.81 m/s²
vmin = m/s
6.Hard
R = 6.5 mh = 30.55 m

A 4 kg cart is released from rest at a height of 30.55 m on a frictionless track and runs through a vertical loop of radius 6.5 m. Use g = 9.81 m/s². Find the normal force Ntop of the track on the cart at the top of the loop.

m = 4 kgh = 30.55 mR = 6.5 mg = 9.81 m/s²
Ntop = N

Answer key

  1. 1. v = 1.728 m/s
  2. 2. vmax = 8.609 m/s
  3. 3. vmax = 13.1 m/s
  4. 4. ω = 1.751 rad/s
  5. 5. vmin = 2.426 m/s
  6. 6. Ntop = 172.7 N

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