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 = 100 m24 m/sF = ?

A 1400 kg car drives around a flat curve of radius 100 m at a constant 24 m/s. Find the inward (centripetal) force Fc needed.

m = 1400 kgv = 24 m/sr = 100 m
Fc = N
2.Easy
r = 200 m13 m/sac​ = ?

A 1500 kg car drives around a flat curve of radius 200 m at a constant 13 m/s. Find its centripetal acceleration ac.

m = 1500 kgv = 13 m/sr = 200 m
ac = m/s²
3.Medium
θ = ?to centre70 km/h

A road engineer wants cars to take a curve of radius 140 m at 70 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 140 mv = 70 km/hg = 9.81 m/s²
θ = °
4.Medium
θ = ?to centre100 km/h

A road engineer wants cars to take a curve of radius 240 m at 100 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 240 mv = 100 km/hg = 9.81 m/s²
θ = °
5.Hard
R = 7 mh = 25.2 m

A 1.5 kg cart is released from rest at a height of 25.2 m on a frictionless track and runs through a vertical loop of radius 7 m. Use g = 9.81 m/s². Find the normal force Ntop of the track on the cart at the top of the loop.

m = 1.5 kgh = 25.2 mR = 7 mg = 9.81 m/s²
Ntop = N
6.Hard
r = 1.3 mv = 5.5 m/s

A 1.3 kg ball on a string 1.3 m long is swung in a vertical circle. At the lowest point it moves at 5.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.3 kgr = 1.3 mv = 5.5 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. Fc = 8064 N
  2. 2. ac = 0.845 m/s²
  3. 3. θ = 15.39 °
  4. 4. θ = 18.15 °
  5. 5. Ntop = 32.37 N
  6. 6. T = 43 N

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