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 = 0.2 mv = ?150 rpm

A small object sits 20 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 = 0.2 m
v = m/s
2.Easy
r = 1.8 mvmax​ = ?

A 0.9 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 20 N. Find the highest speed vmax the stone can have.

m = 0.9 kgr = 1.8 mTmax = 20 N
vmax = m/s
3.Medium
r = 1.7 mω = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 1.7 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.7. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.

r = 1.7 mμs = 0.7g = 9.81 m/s²
ω = rad/s
4.Medium
r = 75 mvmax​ = ?

A car takes a flat curve of radius 75 m. The coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 75 mμs = 0.3g = 9.81 m/s²
vmax = m/s
5.Hard
r = 0.9 mv = ?

A ball on a string 0.9 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 = 0.9 mg = 9.81 m/s²
vmin = m/s
6.Hard
θ = 30°to centrevmax​ = ?

A curve of radius 140 m is banked at 30°, and the coefficient of static friction between tyres and road is 0.1. 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 = 140 mθ = 30°μs = 0.1g = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. v = 3.142 m/s
  2. 2. vmax = 6.325 m/s
  3. 3. ω = 2.871 rad/s
  4. 4. vmax = 14.86 m/s
  5. 5. vmin = 2.971 m/s
  6. 6. vmax = 31.42 m/s

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