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 = 0.5 mvmax​ = ?

A 0.1 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 120 N. Find the highest speed vmax the stone can have.

m = 0.1 kgr = 0.5 mTmax = 120 N
vmax = m/s
3.Medium
r = 45 mvmax​ = ?

A car takes a flat curve of radius 45 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 45 mμs = 0.6g = 9.81 m/s²
vmax = m/s
4.Medium
r = 130 mvmax​ = ?

A car takes a flat curve of radius 130 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 = 130 mμs = 0.7g = 9.81 m/s²
vmax = m/s
5.Hard
r = 1.4 mv = 7.5 m/s

A 0.3 kg ball on a string 1.4 m long is swung in a vertical circle. At the lowest point it moves at 7.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.3 kgr = 1.4 mv = 7.5 m/sg = 9.81 m/s²
T = N
6.Hard
r = 0.6 mv = 3.5 m/s

A 0.8 kg ball on a string 0.6 m long is swung in a vertical circle. At the lowest point it moves at 3.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.8 kgr = 0.6 mv = 3.5 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. rmin = 1389 m
  2. 2. vmax = 24.49 m/s
  3. 3. vmax = 16.27 m/s
  4. 4. vmax = 29.88 m/s
  5. 5. T = 15 N
  6. 6. T = 24.18 N

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