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 = 1.7 mvmax​ = ?

A 1.8 kg stone is whirled in a horizontal circle of radius 1.7 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 = 1.8 kgr = 1.7 mTmax = 90 N
vmax = m/s
2.Easy
r = 2 mvmax​ = ?

A 1.2 kg stone is whirled in a horizontal circle of radius 2 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 = 2 mTmax = 190 N
vmax = m/s
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 = 120 mvmax​ = ?

A car takes a flat curve of radius 120 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 = 120 mμs = 0.6g = 9.81 m/s²
vmax = m/s
5.Hard
r = 1.1 mv = 9 m/s

A 1 kg ball on a string 1.1 m long is swung in a vertical circle. At the lowest point it moves at 9 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1 kgr = 1.1 mv = 9 m/sg = 9.81 m/s²
T = N
6.Hard
r = 1.4 mv = 7.5 m/s

A 1.7 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 = 1.7 kgr = 1.4 mv = 7.5 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. vmax = 9.22 m/s
  2. 2. vmax = 17.8 m/s
  3. 3. vmax = 12.13 m/s
  4. 4. vmax = 26.58 m/s
  5. 5. T = 83.45 N
  6. 6. T = 84.98 N

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