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 = 0.45 mv = ?45 rpm

A small object sits 45 cm from the axis of a disc that turns at a steady 45 revolutions per minute. Find the speed v of the object.

n = 45 rpmr = 0.45 m
v = m/s
2.Easy
r = ?300 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 300 km/h?

v = 300 km/hamax = 1 m/s²
rmin = m
3.Medium
r = 100 mvmax​ = ?

A car takes a flat curve of radius 100 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 = 100 mμs = 0.7g = 9.81 m/s²
vmax = m/s
4.Medium
r = 95 mvmax​ = ?

A car takes a flat curve of radius 95 m. The coefficient of static friction between tyres and road is 0.8. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 95 mμs = 0.8g = 9.81 m/s²
vmax = m/s
5.Hard
r = 1.4 m9 m/svtop​ = ?

A 1.2 kg ball on a light string 1.4 m long is swung in a vertical circle. At the lowest point its speed is 9 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 1.2 kgr = 1.4 mvbottom = 9 m/sg = 9.81 m/s²
Ttop = N
6.Hard
r = 0.7 m10 m/svtop​ = ?

A 0.2 kg ball on a light string 0.7 m long is swung in a vertical circle. At the lowest point its speed is 10 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 0.2 kgr = 0.7 mvbottom = 10 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. v = 2.121 m/s
  2. 2. rmin = 6944 m
  3. 3. vmax = 26.2 m/s
  4. 4. vmax = 27.3 m/s
  5. 5. Ttop = 10.57 N
  6. 6. Ttop = 18.76 N

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