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 = 1.7 mvmax​ = ?

A 0.1 kg stone is whirled in a horizontal circle of radius 1.7 m on a smooth, level table, held by a string that breaks at a tension of 190 N. Find the highest speed vmax the stone can have.

m = 0.1 kgr = 1.7 mTmax = 190 N
vmax = m/s
2.Easy
r = 200 m27 m/sac​ = ?

A 1800 kg car drives around a flat curve of radius 200 m at a constant 27 m/s. Find its centripetal acceleration ac.

m = 1800 kgv = 27 m/sr = 200 m
ac = m/s²
3.Medium
r = 110 mvmax​ = ?

A car takes a flat curve of radius 110 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 110 mμs = 0.6g = 9.81 m/s²
vmax = m/s
4.Medium
L = 0.7 m20°

A small ball on a string of length 0.7 m moves in a horizontal circle so that the string makes a constant angle of 20° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 0.7 mθ = 20°g = 9.81 m/s²
v = m/s
5.Hard
r = 0.5 m7 m/svtop​ = ?

A 0.3 kg ball on a light string 0.5 m long is swung in a vertical circle. At the lowest point its speed is 7 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 0.3 kgr = 0.5 mvbottom = 7 m/sg = 9.81 m/s²
Ttop = 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. vmax = 56.83 m/s
  2. 2. ac = 3.645 m/s²
  3. 3. vmax = 25.45 m/s
  4. 4. v = 0.9246 m/s
  5. 5. Ttop = 14.68 N
  6. 6. vmin = 3.285 m/s

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