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 = ?300 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.5 m/s². What is the smallest radius rmin for a curve taken at 300 km/h?

v = 300 km/hamax = 1.5 m/s²
rmin = m
2.Easy
r = 0.5 mv120 rpm

A small object sits 50 cm from the axis of a disc that turns at a steady 120 revolutions per minute. Find its centripetal acceleration ac.

n = 120 rpmr = 0.5 m
ac = m/s²
3.Medium
r = 3.3 mn = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.3 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.6. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

r = 3.3 mμs = 0.6g = 9.81 m/s²
n = rpm
4.Medium
r = 70 mvmax​ = ?

A car takes a flat curve of radius 70 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 = 70 mμs = 0.6g = 9.81 m/s²
vmax = m/s
5.Hard
r = 1.4 mv = ?

A ball on a string 1.4 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 = 1.4 mg = 9.81 m/s²
vmin = m/s
6.Hard
θ = 30°to centrevmin​ = ?

A curve of radius 210 m is banked at 30°, and the coefficient of static friction between tyres and road is 0.25. Use g = 9.81 m/s². Find the lowest speed vmin at which a car can take the curve without sliding down the bank.

r = 210 mθ = 30°μs = 0.25g = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. rmin = 4630 m
  2. 2. ac = 78.96 m/s²
  3. 3. n = 21.26 rpm
  4. 4. vmax = 20.3 m/s
  5. 5. vmin = 3.706 m/s
  6. 6. vmin = 24.28 m/s

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