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 = 30 m26 m/sac​ = ?

A 1200 kg car drives around a flat curve of radius 30 m at a constant 26 m/s. Find its centripetal acceleration ac.

m = 1200 kgv = 26 m/sr = 30 m
ac = m/s²
2.Easy
r = 1.4 mvmax​ = ?

A 1.5 kg stone is whirled in a horizontal circle of radius 1.4 m on a smooth, level table, held by a string that breaks at a tension of 60 N. Find the highest speed vmax the stone can have.

m = 1.5 kgr = 1.4 mTmax = 60 N
vmax = m/s
3.Medium
r = 1.6 mn = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 1.6 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.6. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

r = 1.6 mμs = 0.6g = 9.81 m/s²
n = rpm
4.Medium
L = 1.7 m60°

A small ball on a string of length 1.7 m moves in a horizontal circle so that the string makes a constant angle of 60° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 1.7 mθ = 60°g = 9.81 m/s²
T = s
5.Hard
r = 1 mv = ?

A ball on a string 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 mg = 9.81 m/s²
vmin = m/s
6.Hard
θ = 12°to centrevmin​ = ?

A curve of radius 280 m is banked at 12°, and the coefficient of static friction between tyres and road is 0.15. Use g = 9.81 m/s². Find the lowest speed vmin at which a car can take the curve without sliding down the bank.

r = 280 mθ = 12°μs = 0.15g = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. ac = 22.53 m/s²
  2. 2. vmax = 7.483 m/s
  3. 3. n = 30.53 rpm
  4. 4. T = 1.85 s
  5. 5. vmin = 3.132 m/s
  6. 6. vmin = 12.9 m/s

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