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 = 50 m29 m/sF = ?

A 900 kg car drives around a flat curve of radius 50 m at a constant 29 m/s. Find the inward (centripetal) force Fc needed.

m = 900 kgv = 29 m/sr = 50 m
Fc = N
2.Easy
r = 1.25 mv200 rpm

A small object sits 125 cm from the axis of a disc that turns at a steady 200 revolutions per minute. Find its centripetal acceleration ac.

n = 200 rpmr = 1.25 m
ac = m/s²
3.Medium
r = 55 mvmax​ = ?

A car takes a flat curve of radius 55 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 = 55 mμs = 0.8g = 9.81 m/s²
vmax = m/s
4.Medium
r = 110 mvmax​ = ?

A car takes a flat curve of radius 110 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 = 110 mμs = 0.3g = 9.81 m/s²
vmax = m/s
5.Hard
r = 1.5 mv = 4.5 m/s

A 0.8 kg ball on a string 1.5 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 = 0.8 kgr = 1.5 mv = 4.5 m/sg = 9.81 m/s²
T = N
6.Hard
r = 0.7 m10 m/svtop​ = ?

A 1.5 kg ball on a light string 0.7 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 = 1.5 kgr = 0.7 mvbottom = 10 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. Fc = 15138 N
  2. 2. ac = 548.3 m/s²
  3. 3. vmax = 20.78 m/s
  4. 4. vmax = 17.99 m/s
  5. 5. T = 18.65 N
  6. 6. Ttop = 140.7 N

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