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 = ?300 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.5 m/s². What is the smallest radius rmin for a curve taken at 300 km/h?

v = 300 km/hamax = 0.5 m/s²
rmin = m
2.Easy
r = ?200 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1 m/s². What is the smallest radius rmin for a curve taken at 200 km/h?

v = 200 km/hamax = 1 m/s²
rmin = m
3.Medium
r = 105 mvmax​ = ?

A car takes a flat curve of radius 105 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 105 mμs = 0.6g = 9.81 m/s²
vmax = m/s
4.Medium
r = 60 mvmax​ = ?

A car takes a flat curve of radius 60 m. The coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 60 mμs = 0.3g = 9.81 m/s²
vmax = m/s
5.Hard
r = 0.9 m9.5 m/svtop​ = ?

A 1 kg ball on a light string 0.9 m long is swung in a vertical circle. At the lowest point its speed is 9.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 1 kgr = 0.9 mvbottom = 9.5 m/sg = 9.81 m/s²
Ttop = N
6.Hard
r = 1 m12 m/svtop​ = ?

A 1.8 kg ball on a light string 1 m long is swung in a vertical circle. At the lowest point its speed is 12 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 1.8 kgr = 1 mvbottom = 12 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. rmin = 13889 m
  2. 2. rmin = 3086 m
  3. 3. vmax = 24.86 m/s
  4. 4. vmax = 13.29 m/s
  5. 5. Ttop = 51.23 N
  6. 6. Ttop = 170.9 N

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