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 mvmax​ = ?

A 0.1 kg stone is whirled in a horizontal circle of radius 1 m on a smooth, level table, held by a string that breaks at a tension of 10 N. Find the highest speed vmax the stone can have.

m = 0.1 kgr = 1 mTmax = 10 N
vmax = m/s
2.Easy
r = 80 m13 m/sF = ?

An 800 kg car drives around a flat curve of radius 80 m at a constant 13 m/s. Find the inward (centripetal) force Fc needed.

m = 800 kgv = 13 m/sr = 80 m
Fc = N
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 0.6. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 125 mμs = 0.6g = 9.81 m/s²
vmax = m/s
4.Medium
r = 35 mvmax​ = ?

A car takes a flat curve of radius 35 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 = 35 mμs = 0.8g = 9.81 m/s²
vmax = m/s
5.Hard
r = 1.3 m10 m/svtop​ = ?

A 1.2 kg ball on a light string 1.3 m long is swung in a vertical circle. At the lowest point its speed is 10 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 1.2 kgr = 1.3 mvbottom = 10 m/sg = 9.81 m/s²
Ttop = N
6.Hard
r = 0.5 mv = 9 m/s

A 0.7 kg ball on a string 0.5 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 = 0.7 kgr = 0.5 mv = 9 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. vmax = 10 m/s
  2. 2. Fc = 1690 N
  3. 3. vmax = 27.12 m/s
  4. 4. vmax = 16.57 m/s
  5. 5. Ttop = 33.45 N
  6. 6. T = 120.3 N

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