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 = ?300 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.5 m/s². What is the smallest radius rmin for a curve taken at 300 km/h?

v = 300 km/hamax = 1.5 m/s²
rmin = m
2.Easy
r = 0.4 mvmax​ = ?

A 1.6 kg stone is whirled in a horizontal circle of radius 0.4 m on a smooth, level table, held by a string that breaks at a tension of 100 N. Find the highest speed vmax the stone can have.

m = 1.6 kgr = 0.4 mTmax = 100 N
vmax = m/s
3.Medium
r = 65 mvmax​ = ?

A car takes a flat curve of radius 65 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 = 65 mμs = 0.5g = 9.81 m/s²
vmax = m/s
4.Medium
r = 125 mvmax​ = ?

A car takes a flat curve of radius 125 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 = 125 mμs = 0.8g = 9.81 m/s²
vmax = m/s
5.Hard
r = 0.8 mv = 6 m/s

A 1.7 kg ball on a string 0.8 m long is swung in a vertical circle. At the lowest point it moves at 6 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.7 kgr = 0.8 mv = 6 m/sg = 9.81 m/s²
T = N
6.Hard
r = 0.9 mv = 4.5 m/s

A 1.2 kg ball on a string 0.9 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 = 1.2 kgr = 0.9 mv = 4.5 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. rmin = 4630 m
  2. 2. vmax = 5 m/s
  3. 3. vmax = 17.86 m/s
  4. 4. vmax = 31.32 m/s
  5. 5. T = 93.18 N
  6. 6. T = 38.77 N

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