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 = ?120 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.8 m/s². What is the smallest radius rmin for a curve taken at 120 km/h?

v = 120 km/hamax = 0.8 m/s²
rmin = m
2.Easy
r = ?200 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1 m/s². What is the smallest radius rmin for a curve taken at 200 km/h?

v = 200 km/hamax = 1 m/s²
rmin = m
3.Medium
r = 120 mvmax​ = ?

A car takes a flat curve of radius 120 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 = 120 mμs = 0.7g = 9.81 m/s²
vmax = m/s
4.Medium
L = 1 m50°

A small ball on a string of length 1 m moves in a horizontal circle so that the string makes a constant angle of 50° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 1 mθ = 50°g = 9.81 m/s²
v = m/s
5.Hard
θ = 15°to centrevmin​ = ?

A curve of radius 190 m is banked at 15°, and the coefficient of static friction between tyres and road is 0.2. 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 = 190 mθ = 15°μs = 0.2g = 9.81 m/s²
vmin = m/s
6.Hard
r = 0.6 mv = 4.5 m/s

A 0.5 kg ball on a string 0.6 m long is swung in a vertical circle. At the lowest point it moves at 4.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.5 kgr = 0.6 mv = 4.5 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. rmin = 1389 m
  2. 2. rmin = 3086 m
  3. 3. vmax = 28.71 m/s
  4. 4. v = 2.993 m/s
  5. 5. vmin = 10.96 m/s
  6. 6. T = 21.78 N

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