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 = 80 m13 m/sac​ = ?

A 1500 kg car drives around a flat curve of radius 80 m at a constant 13 m/s. Find its centripetal acceleration ac.

m = 1500 kgv = 13 m/sr = 80 m
ac = m/s²
2.Easy
r = 1.25 mv150 rpm

A small object sits 125 cm from the axis of a disc that turns at a steady 150 revolutions per minute. Find its centripetal acceleration ac.

n = 150 rpmr = 1.25 m
ac = m/s²
3.Medium
θ = 18°to centrev = ?

A curve of radius 300 m is banked at 18°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 300 mθ = 18°g = 9.81 m/s²
v = m/s
4.Medium
θ = ?to centre50 km/h

A road engineer wants cars to take a curve of radius 310 m at 50 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 310 mv = 50 km/hg = 9.81 m/s²
θ = °
5.Hard
r = 1 mv = 8 m/s

A 2 kg ball on a string 1 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 = 2 kgr = 1 mv = 8 m/sg = 9.81 m/s²
T = N
6.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

Answer key

  1. 1. ac = 2.112 m/s²
  2. 2. ac = 308.4 m/s²
  3. 3. v = 30.92 m/s
  4. 4. θ = 3.629 °
  5. 5. T = 147.6 N
  6. 6. vmin = 3.132 m/s

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