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 = 1.25 mv = ?78 rpm

A small object sits 125 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 = 1.25 m
v = m/s
2.Easy
r = 1.8 mvmax​ = ?

A 1.2 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 50 N. Find the highest speed vmax the stone can have.

m = 1.2 kgr = 1.8 mTmax = 50 N
vmax = m/s
3.Medium
r = 30 mvmax​ = ?

A car takes a flat curve of radius 30 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 30 mμs = 0.6g = 9.81 m/s²
vmax = m/s
4.Medium
r = 45 mvmax​ = ?

A car takes a flat curve of radius 45 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 = 45 mμs = 0.3g = 9.81 m/s²
vmax = m/s
5.Hard
θ = 15°to centrevmax​ = ?

A curve of radius 70 m is banked at 15°, and 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 a car can take the curve without sliding up and out.

r = 70 mθ = 15°μs = 0.4g = 9.81 m/s²
vmax = m/s
6.Hard
r = 0.7 mv = 6.5 m/s

A 1.1 kg ball on a string 0.7 m long is swung in a vertical circle. At the lowest point it moves at 6.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.1 kgr = 0.7 mv = 6.5 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. v = 10.21 m/s
  2. 2. vmax = 8.66 m/s
  3. 3. vmax = 13.29 m/s
  4. 4. vmax = 11.51 m/s
  5. 5. vmax = 22.67 m/s
  6. 6. T = 77.18 N

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