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 = 100 m10 m/sac​ = ?

A 1300 kg car drives around a flat curve of radius 100 m at a constant 10 m/s. Find its centripetal acceleration ac.

m = 1300 kgv = 10 m/sr = 100 m
ac = m/s²
2.Easy
r = 60 m22 m/sac​ = ?

A 1700 kg car drives around a flat curve of radius 60 m at a constant 22 m/s. Find its centripetal acceleration ac.

m = 1700 kgv = 22 m/sr = 60 m
ac = m/s²
3.Medium
L = 0.8 m50°

A small ball on a string of length 0.8 m moves in a horizontal circle so that the string makes a constant angle of 50° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 0.8 mθ = 50°g = 9.81 m/s²
T = 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 0.7. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 110 mμs = 0.7g = 9.81 m/s²
vmax = m/s
5.Hard
θ = 18°to centrevmin​ = ?

A curve of radius 100 m is banked at 18°, and the coefficient of static friction between tyres and road is 0.1. 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 = 100 mθ = 18°μs = 0.1g = 9.81 m/s²
vmin = m/s
6.Hard
r = 1.5 m11 m/svtop​ = ?

A 1 kg ball on a light string 1.5 m long is swung in a vertical circle. At the lowest point its speed is 11 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 kgr = 1.5 mvbottom = 11 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. ac = 1 m/s²
  2. 2. ac = 8.067 m/s²
  3. 3. T = 1.439 s
  4. 4. vmax = 27.48 m/s
  5. 5. vmin = 14.62 m/s
  6. 6. Ttop = 31.62 N

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