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 = 1.1 mv = ?33 rpm

A small object sits 110 cm from the axis of a disc that turns at a steady 33 revolutions per minute. Find the speed v of the object.

n = 33 rpmr = 1.1 m
v = m/s
2.Easy
r = 0.5 mvmax​ = ?

A 1.1 kg stone is whirled in a horizontal circle of radius 0.5 m on a smooth, level table, held by a string that breaks at a tension of 180 N. Find the highest speed vmax the stone can have.

m = 1.1 kgr = 0.5 mTmax = 180 N
vmax = m/s
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 0.4. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 105 mμs = 0.4g = 9.81 m/s²
vmax = m/s
4.Medium
r = 150 mvmax​ = ?

A car takes a flat curve of radius 150 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 = 150 mμs = 0.4g = 9.81 m/s²
vmax = m/s
5.Hard
r = 0.6 m10 m/svtop​ = ?

A 1.3 kg ball on a light string 0.6 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 = 1.3 kgr = 0.6 mvbottom = 10 m/sg = 9.81 m/s²
Ttop = N
6.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

Answer key

  1. 1. v = 3.801 m/s
  2. 2. vmax = 9.045 m/s
  3. 3. vmax = 20.3 m/s
  4. 4. vmax = 24.26 m/s
  5. 5. Ttop = 152.9 N
  6. 6. vmin = 3.431 m/s

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