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 = 130 m20 m/sF = ?

A 1300 kg car drives around a flat curve of radius 130 m at a constant 20 m/s. Find the inward (centripetal) force Fc needed.

m = 1300 kgv = 20 m/sr = 130 m
Fc = N
2.Easy
r = 0.3 mvmax​ = ?

A 0.9 kg stone is whirled in a horizontal circle of radius 0.3 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 = 0.9 kgr = 0.3 mTmax = 100 N
vmax = m/s
3.Medium
r = 2.2 mω = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.2 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.3. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.

r = 2.2 mμs = 0.3g = 9.81 m/s²
ω = rad/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 0.3. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 115 mμs = 0.3g = 9.81 m/s²
vmax = m/s
5.Hard
r = 0.6 mv = 6 m/s

A 1.8 kg ball on a string 0.6 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 = 1.8 kgr = 0.6 mv = 6 m/sg = 9.81 m/s²
T = N
6.Hard
r = 1.1 mv = ?

A ball on a string 1.1 m long is swung in a vertical circle. Use g = 9.81 m/s². What is the smallest speed vmin at the top for which the string just stays tight?

r = 1.1 mg = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. Fc = 4000 N
  2. 2. vmax = 5.774 m/s
  3. 3. ω = 3.855 rad/s
  4. 4. vmax = 18.4 m/s
  5. 5. T = 125.7 N
  6. 6. vmin = 3.285 m/s

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