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 = ?200 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.2 m/s². What is the smallest radius rmin for a curve taken at 200 km/h?

v = 200 km/hamax = 1.2 m/s²
rmin = m
2.Easy
r = ?250 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.5 m/s². What is the smallest radius rmin for a curve taken at 250 km/h?

v = 250 km/hamax = 0.5 m/s²
rmin = m
3.Medium
r = 115 mvmax​ = ?

A car takes a flat curve of radius 115 m. The coefficient of static friction between tyres and road is 0.8. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 115 mμs = 0.8g = 9.81 m/s²
vmax = m/s
4.Medium
r = 55 mvmax​ = ?

A car takes a flat curve of radius 55 m. The coefficient of static friction between tyres and road is 0.7. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 55 mμs = 0.7g = 9.81 m/s²
vmax = m/s
5.Hard
r = 1 mv = ?

A ball on a string 1 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 mg = 9.81 m/s²
vmin = m/s
6.Hard
θ = 30°to centrevmin​ = ?

A curve of radius 150 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 = 150 mθ = 30°μs = 0.25g = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. rmin = 2572 m
  2. 2. rmin = 9645 m
  3. 3. vmax = 30.04 m/s
  4. 4. vmax = 19.43 m/s
  5. 5. vmin = 3.132 m/s
  6. 6. vmin = 20.52 m/s

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