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 = 0.9 mv = ?200 rpm

A small object sits 90 cm from the axis of a disc that turns at a steady 200 revolutions per minute. Find the speed v of the object.

n = 200 rpmr = 0.9 m
v = m/s
2.Easy
r = 70 m10 m/sac​ = ?

A 900 kg car drives around a flat curve of radius 70 m at a constant 10 m/s. Find its centripetal acceleration ac.

m = 900 kgv = 10 m/sr = 70 m
ac = m/s²
3.Medium
L = 1.5 m45°

A small ball on a string of length 1.5 m moves in a horizontal circle so that the string makes a constant angle of 45° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 1.5 mθ = 45°g = 9.81 m/s²
v = m/s
4.Medium
θ = ?to centre90 km/h

A road engineer wants cars to take a curve of radius 120 m at 90 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 120 mv = 90 km/hg = 9.81 m/s²
θ = °
5.Hard
r = 0.7 mv = ?

A ball on a string 0.7 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 = 0.7 mg = 9.81 m/s²
vmin = m/s
6.Hard
r = 0.8 mv = 8 m/s

A 0.7 kg ball on a string 0.8 m long is swung in a vertical circle. At the lowest point it moves at 8 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.7 kgr = 0.8 mv = 8 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. v = 18.85 m/s
  2. 2. ac = 1.429 m/s²
  3. 3. v = 3.226 m/s
  4. 4. θ = 27.96 °
  5. 5. vmin = 2.62 m/s
  6. 6. T = 62.87 N

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