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 = 160 m24 m/sF = ?

A 1400 kg car drives around a flat curve of radius 160 m at a constant 24 m/s. Find the inward (centripetal) force Fc needed.

m = 1400 kgv = 24 m/sr = 160 m
Fc = N
2.Easy
r = 1.6 mvmax​ = ?

A 0.8 kg stone is whirled in a horizontal circle of radius 1.6 m on a smooth, level table, held by a string that breaks at a tension of 30 N. Find the highest speed vmax the stone can have.

m = 0.8 kgr = 1.6 mTmax = 30 N
vmax = m/s
3.Medium
L = 0.9 m15°

A small ball on a string of length 0.9 m moves in a horizontal circle so that the string makes a constant angle of 15° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 0.9 mθ = 15°g = 9.81 m/s²
T = s
4.Medium
r = 25 mvmax​ = ?

A car takes a flat curve of radius 25 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 = 25 mμs = 0.3g = 9.81 m/s²
vmax = m/s
5.Hard
θ = 12°to centrevmax​ = ?

A curve of radius 40 m is banked at 12°, and 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 a car can take the curve without sliding up and out.

r = 40 mθ = 12°μs = 0.4g = 9.81 m/s²
vmax = m/s
6.Hard
r = 0.9 mv = 7.5 m/s

A 0.5 kg ball on a string 0.9 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 = 0.5 kgr = 0.9 mv = 7.5 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. Fc = 5040 N
  2. 2. vmax = 7.746 m/s
  3. 3. T = 1.87 s
  4. 4. vmax = 8.578 m/s
  5. 5. vmax = 16.21 m/s
  6. 6. T = 36.16 N

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