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 = 0.3 mv60 rpm

A small object sits 30 cm from the axis of a disc that turns at a steady 60 revolutions per minute. Find its centripetal acceleration ac.

n = 60 rpmr = 0.3 m
ac = m/s²
2.Easy
r = 160 m21 m/sac​ = ?

A 1600 kg car drives around a flat curve of radius 160 m at a constant 21 m/s. Find its centripetal acceleration ac.

m = 1600 kgv = 21 m/sr = 160 m
ac = m/s²
3.Medium
θ = ?to centre80 km/h

A road engineer wants cars to take a curve of radius 370 m at 80 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 370 mv = 80 km/hg = 9.81 m/s²
θ = °
4.Medium
θ = 20°to centrev = ?

A curve of radius 180 m is banked at 20°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 180 mθ = 20°g = 9.81 m/s²
v = m/s
5.Hard
R = 7 mh = ?

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 7 m. From what minimum height hmin above the bottom of the loop must it start to stay on the track at the top of the loop?

R = 7 mv₀ = 0
hmin = m
6.Hard
r = 1.3 mv = 3.5 m/s

A 0.9 kg ball on a string 1.3 m long is swung in a vertical circle. At the lowest point it moves at 3.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.9 kgr = 1.3 mv = 3.5 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. ac = 11.84 m/s²
  2. 2. ac = 2.756 m/s²
  3. 3. θ = 7.748 °
  4. 4. v = 25.35 m/s
  5. 5. hmin = 17.5 m
  6. 6. T = 17.31 N

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