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 = 140 m19 m/sac​ = ?

A 600 kg car drives around a flat curve of radius 140 m at a constant 19 m/s. Find its centripetal acceleration ac.

m = 600 kgv = 19 m/sr = 140 m
ac = m/s²
2.Easy
r = 200 m22 m/sF = ?

A 1200 kg car drives around a flat curve of radius 200 m at a constant 22 m/s. Find the inward (centripetal) force Fc needed.

m = 1200 kgv = 22 m/sr = 200 m
Fc = N
3.Medium
r = 140 mvmax​ = ?

A car takes a flat curve of radius 140 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 = 140 mμs = 0.8g = 9.81 m/s²
vmax = m/s
4.Medium
L = 0.5 m40°

A small ball on a string of length 0.5 m moves in a horizontal circle so that the string makes a constant angle of 40° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 0.5 mθ = 40°g = 9.81 m/s²
T = s
5.Hard
r = 0.7 mv = 6 m/s

A 0.2 kg ball on a string 0.7 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 = 0.2 kgr = 0.7 mv = 6 m/sg = 9.81 m/s²
T = N
6.Hard
r = 1.1 m9 m/svtop​ = ?

A 2 kg ball on a light string 1.1 m long is swung in a vertical circle. At the lowest point its speed is 9 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 2 kgr = 1.1 mvbottom = 9 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. ac = 2.579 m/s²
  2. 2. Fc = 2904 N
  3. 3. vmax = 33.15 m/s
  4. 4. T = 1.242 s
  5. 5. T = 12.25 N
  6. 6. Ttop = 49.17 N

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