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 = ?240 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 240 km/h?

v = 240 km/hamax = 1 m/s²
rmin = m
2.Easy
r = 1.2 mvmax​ = ?

A 0.8 kg stone is whirled in a horizontal circle of radius 1.2 m on a smooth, level table, held by a string that breaks at a tension of 200 N. Find the highest speed vmax the stone can have.

m = 0.8 kgr = 1.2 mTmax = 200 N
vmax = m/s
3.Medium
L = 0.8 m60°

A small ball on a string of length 0.8 m moves in a horizontal circle so that the string makes a constant angle of 60° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 0.8 mθ = 60°g = 9.81 m/s²
v = m/s
4.Medium
r = 35 mvmax​ = ?

A car takes a flat curve of radius 35 m. 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 the car can take the curve without skidding.

r = 35 mμs = 0.4g = 9.81 m/s²
vmax = m/s
5.Hard
θ = 20°to centrevmax​ = ?

A curve of radius 100 m is banked at 20°, and 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 a car can take the curve without sliding up and out.

r = 100 mθ = 20°μs = 0.3g = 9.81 m/s²
vmax = m/s
6.Hard
r = 0.8 mv = ?

A ball on a string 0.8 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 = 0.8 mg = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. rmin = 4444 m
  2. 2. vmax = 17.32 m/s
  3. 3. v = 3.431 m/s
  4. 4. vmax = 11.72 m/s
  5. 5. vmax = 27.04 m/s
  6. 6. vmin = 2.801 m/s

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