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 1.7 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 90 N. Find the highest speed vmax the stone can have.

m = 1.7 kgr = 0.5 mTmax = 90 N
vmax = m/s
2.Easy
r = 1.4 mvmax​ = ?

A 1.7 kg stone is whirled in a horizontal circle of radius 1.4 m on a smooth, level table, held by a string that breaks at a tension of 160 N. Find the highest speed vmax the stone can have.

m = 1.7 kgr = 1.4 mTmax = 160 N
vmax = m/s
3.Medium
r = 125 mvmax​ = ?

A car takes a flat curve of radius 125 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 125 mμs = 0.4g = 9.81 m/s²
vmax = m/s
4.Medium
r = 115 mvmax​ = ?

A car takes a flat curve of radius 115 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 = 115 mμs = 0.8g = 9.81 m/s²
vmax = m/s
5.Hard
r = 1.1 mv = 5.5 m/s

A 0.3 kg ball on a string 1.1 m long is swung in a vertical circle. At the lowest point it moves at 5.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.3 kgr = 1.1 mv = 5.5 m/sg = 9.81 m/s²
T = N
6.Hard
r = 1.4 mv = 5.5 m/s

A 1.2 kg ball on a string 1.4 m long is swung in a vertical circle. At the lowest point it moves at 5.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.2 kgr = 1.4 mv = 5.5 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. vmax = 5.145 m/s
  2. 2. vmax = 11.48 m/s
  3. 3. vmax = 22.15 m/s
  4. 4. vmax = 30.04 m/s
  5. 5. T = 11.19 N
  6. 6. T = 37.7 N

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