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 = 1.9 mvmax​ = ?

A 0.9 kg stone is whirled in a horizontal circle of radius 1.9 m on a smooth, level table, held by a string that breaks at a tension of 120 N. Find the highest speed vmax the stone can have.

m = 0.9 kgr = 1.9 mTmax = 120 N
vmax = m/s
2.Easy
r = 1.5 mvmax​ = ?

A 1.6 kg stone is whirled in a horizontal circle of radius 1.5 m on a smooth, level table, held by a string that breaks at a tension of 190 N. Find the highest speed vmax the stone can have.

m = 1.6 kgr = 1.5 mTmax = 190 N
vmax = m/s
3.Medium
r = 120 mvmax​ = ?

A car drives over the top of a hump in the road, which is a circular arc of radius 120 m. Use g = 9.81 m/s². Above what speed vmax do the wheels leave the road at the top?

r = 120 mg = 9.81 m/s²
vmax = m/s
4.Medium
r = 40 m6 m/s

A 1300 kg car drives over the top of a hump in the road at 6 m/s. The top of the hump is a circular arc of radius 40 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1300 kgv = 6 m/sr = 40 mg = 9.81 m/s²
N = N
5.Hard
R = 4.5 mh = 15.3 m

A 3.5 kg cart is released from rest at a height of 15.3 m on a frictionless track and runs through a vertical loop of radius 4.5 m. Use g = 9.81 m/s². Find the normal force Ntop of the track on the cart at the top of the loop.

m = 3.5 kgh = 15.3 mR = 4.5 mg = 9.81 m/s²
Ntop = N
6.Hard
R = 7 mh = 28.7 m

A 0.5 kg cart is released from rest at a height of 28.7 m on a frictionless track and runs through a vertical loop of radius 7 m. Use g = 9.81 m/s². Find the normal force Ntop of the track on the cart at the top of the loop.

m = 0.5 kgh = 28.7 mR = 7 mg = 9.81 m/s²
Ntop = N

Answer key

  1. 1. vmax = 15.92 m/s
  2. 2. vmax = 13.35 m/s
  3. 3. vmax = 34.31 m/s
  4. 4. N = 11583 N
  5. 5. Ntop = 61.8 N
  6. 6. Ntop = 15.7 N

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