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 = 0.5 mvmax​ = ?

A 1.2 kg stone is whirled in a horizontal circle of radius 0.5 m on a smooth, level table, held by a string that breaks at a tension of 190 N. Find the highest speed vmax the stone can have.

m = 1.2 kgr = 0.5 mTmax = 190 N
vmax = m/s
2.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
3.Medium
r = 50 mvmax​ = ?

A car takes a flat curve of radius 50 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 = 50 mμs = 0.3g = 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 0.5. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 45 mμs = 0.5g = 9.81 m/s²
vmax = m/s
5.Hard
θ = 25°to centrevmin​ = ?

A curve of radius 80 m is banked at 25°, and the coefficient of static friction between tyres and road is 0.4. 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 = 80 mθ = 25°μs = 0.4g = 9.81 m/s²
vmin = m/s
6.Hard
r = 1.5 mv = 4 m/s

A 1.2 kg ball on a string 1.5 m long is swung in a vertical circle. At the lowest point it moves at 4 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.2 kgr = 1.5 mv = 4 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. vmax = 8.898 m/s
  2. 2. rmin = 4444 m
  3. 3. vmax = 12.13 m/s
  4. 4. vmax = 14.86 m/s
  5. 5. vmin = 6.623 m/s
  6. 6. T = 24.57 N

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