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 m24 m/sF = ?

A 1600 kg car drives around a flat curve of radius 80 m at a constant 24 m/s. Find the inward (centripetal) force Fc needed.

m = 1600 kgv = 24 m/sr = 80 m
Fc = N
2.Easy
r = 50 m17 m/sF = ?

A 1100 kg car drives around a flat curve of radius 50 m at a constant 17 m/s. Find the inward (centripetal) force Fc needed.

m = 1100 kgv = 17 m/sr = 50 m
Fc = N
3.Medium
r = 145 mvmax​ = ?

A car takes a flat curve of radius 145 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 145 mμs = 0.4g = 9.81 m/s²
vmax = m/s
4.Medium
θ = ?to centre80 km/h

A road engineer wants cars to take a curve of radius 270 m at 80 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 270 mv = 80 km/hg = 9.81 m/s²
θ = °
5.Hard
r = 1.2 mv = ?

A ball on a string 1.2 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 = 1.2 mg = 9.81 m/s²
vmin = m/s
6.Hard
r = 1.1 mv = 4 m/s

A 0.5 kg ball on a string 1.1 m long is swung in a vertical circle. At the lowest point it moves at 4 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.5 kgr = 1.1 mv = 4 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. Fc = 11520 N
  2. 2. Fc = 6358 N
  3. 3. vmax = 23.85 m/s
  4. 4. θ = 10.56 °
  5. 5. vmin = 3.431 m/s
  6. 6. T = 12.18 N

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