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 mvmax​ = ?

A 1.5 kg stone is whirled in a horizontal circle of radius 1.1 m on a smooth, level table, held by a string that breaks at a tension of 10 N. Find the highest speed vmax the stone can have.

m = 1.5 kgr = 1.1 mTmax = 10 N
vmax = m/s
2.Easy
r = 40 m11 m/sF = ?

A 700 kg car drives around a flat curve of radius 40 m at a constant 11 m/s. Find the inward (centripetal) force Fc needed.

m = 700 kgv = 11 m/sr = 40 m
Fc = N
3.Medium
r = 80 mvmax​ = ?

A car takes a flat curve of radius 80 m. The coefficient of static friction between tyres and road is 0.5. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 80 mμs = 0.5g = 9.81 m/s²
vmax = m/s
4.Medium
r = 40 mvmax​ = ?

A car takes a flat curve of radius 40 m. The coefficient of static friction between tyres and road is 0.5. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 40 mμs = 0.5g = 9.81 m/s²
vmax = m/s
5.Hard
R = 8.5 mh = 29.75 m

A 3 kg cart is released from rest at a height of 29.75 m on a frictionless track and runs through a vertical loop of radius 8.5 m. Use g = 9.81 m/s². Find the normal force Nbottom of the track on the cart at the bottom of the loop.

m = 3 kgh = 29.75 mR = 8.5 mg = 9.81 m/s²
Nbottom = N
6.Hard
r = 0.6 m8 m/svtop​ = ?

A 1 kg ball on a light string 0.6 m long is swung in a vertical circle. At the lowest point its speed is 8 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 = 0.6 mvbottom = 8 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. vmax = 2.708 m/s
  2. 2. Fc = 2118 N
  3. 3. vmax = 19.81 m/s
  4. 4. vmax = 14.01 m/s
  5. 5. Nbottom = 235.4 N
  6. 6. Ttop = 57.62 N

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