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 = 180 m28 m/sac​ = ?

A 1300 kg car drives around a flat curve of radius 180 m at a constant 28 m/s. Find its centripetal acceleration ac.

m = 1300 kgv = 28 m/sr = 180 m
ac = m/s²
2.Easy
r = 40 m24 m/sF = ?

A 1200 kg car drives around a flat curve of radius 40 m at a constant 24 m/s. Find the inward (centripetal) force Fc needed.

m = 1200 kgv = 24 m/sr = 40 m
Fc = N
3.Medium
θ = ?to centre40 km/h

A road engineer wants cars to take a curve of radius 240 m at 40 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 240 mv = 40 km/hg = 9.81 m/s²
θ = °
4.Medium
θ = ?to centre120 km/h

A road engineer wants cars to take a curve of radius 160 m at 120 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 160 mv = 120 km/hg = 9.81 m/s²
θ = °
5.Hard
r = 0.7 mv = 6.5 m/s

A 2 kg ball on a string 0.7 m long is swung in a vertical circle. At the lowest point it moves at 6.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 2 kgr = 0.7 mv = 6.5 m/sg = 9.81 m/s²
T = N
6.Hard
θ = 25°to centrevmax​ = ?

A curve of radius 160 m is banked at 25°, and the coefficient of static friction between tyres and road is 0.25. Use g = 9.81 m/s². Find the highest speed vmax at which a car can take the curve without sliding up and out.

r = 160 mθ = 25°μs = 0.25g = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. ac = 4.356 m/s²
  2. 2. Fc = 17280 N
  3. 3. θ = 3.002 °
  4. 4. θ = 35.29 °
  5. 5. T = 140.3 N
  6. 6. vmax = 35.67 m/s

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