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 = ?160 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.2 m/s². What is the smallest radius rmin for a curve taken at 160 km/h?

v = 160 km/hamax = 1.2 m/s²
rmin = m
2.Easy
r = 90 m14 m/sF = ?

A 600 kg car drives around a flat curve of radius 90 m at a constant 14 m/s. Find the inward (centripetal) force Fc needed.

m = 600 kgv = 14 m/sr = 90 m
Fc = N
3.Medium
θ = 20°to centrev = ?

A curve of radius 60 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 = 60 mθ = 20°g = 9.81 m/s²
v = m/s
4.Medium
r = 145 mvmax​ = ?

A car takes a flat curve of radius 145 m. The coefficient of static friction between tyres and road is 0.7. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 145 mμs = 0.7g = 9.81 m/s²
vmax = m/s
5.Hard
r = 0.6 mv = 7.5 m/s

A 0.2 kg ball on a string 0.6 m long is swung in a vertical circle. At the lowest point it moves at 7.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.2 kgr = 0.6 mv = 7.5 m/sg = 9.81 m/s²
T = N
6.Hard
r = 1 mv = 9 m/s

A 0.4 kg ball on a string 1 m long is swung in a vertical circle. At the lowest point it moves at 9 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.4 kgr = 1 mv = 9 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. rmin = 1646 m
  2. 2. Fc = 1307 N
  3. 3. v = 14.64 m/s
  4. 4. vmax = 31.55 m/s
  5. 5. T = 20.71 N
  6. 6. T = 36.32 N

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