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 = 100 m17 m/sac​ = ?

A 900 kg car drives around a flat curve of radius 100 m at a constant 17 m/s. Find its centripetal acceleration ac.

m = 900 kgv = 17 m/sr = 100 m
ac = m/s²
2.Easy
r = 1.6 mvmax​ = ?

A 1.7 kg stone is whirled in a horizontal circle of radius 1.6 m on a smooth, level table, held by a string that breaks at a tension of 50 N. Find the highest speed vmax the stone can have.

m = 1.7 kgr = 1.6 mTmax = 50 N
vmax = m/s
3.Medium
L = 0.9 m15°

A small ball on a string of length 0.9 m moves in a horizontal circle so that the string makes a constant angle of 15° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 0.9 mθ = 15°g = 9.81 m/s²
v = m/s
4.Medium
r = 60 m12 m/s

A 1700 kg car drives over the top of a hump in the road at 12 m/s. The top of the hump is a circular arc of radius 60 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1700 kgv = 12 m/sr = 60 mg = 9.81 m/s²
N = N
5.Hard
R = 5 mh = 19.5 m

A 0.5 kg cart is released from rest at a height of 19.5 m on a frictionless track and runs through a vertical loop of radius 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 = 0.5 kgh = 19.5 mR = 5 mg = 9.81 m/s²
Nbottom = N
6.Hard
R = 8 mh = 36.8 m

A 2 kg cart is released from rest at a height of 36.8 m on a frictionless track and runs through a vertical loop of radius 8 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 = 2 kgh = 36.8 mR = 8 mg = 9.81 m/s²
Nbottom = N

Answer key

  1. 1. ac = 2.89 m/s²
  2. 2. vmax = 6.86 m/s
  3. 3. v = 0.7825 m/s
  4. 4. N = 12597 N
  5. 5. Nbottom = 43.16 N
  6. 6. Nbottom = 200.1 N

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