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 = 0.15 mv30 rpm

A small object sits 15 cm from the axis of a disc that turns at a steady 30 revolutions per minute. Find its centripetal acceleration ac.

n = 30 rpmr = 0.15 m
ac = m/s²
2.Easy
r = 170 m22 m/sac​ = ?

A 1100 kg car drives around a flat curve of radius 170 m at a constant 22 m/s. Find its centripetal acceleration ac.

m = 1100 kgv = 22 m/sr = 170 m
ac = m/s²
3.Medium
r = 135 mvmax​ = ?

A car takes a flat curve of radius 135 m. The coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 135 mμs = 0.3g = 9.81 m/s²
vmax = m/s
4.Medium
r = 120 mvmax​ = ?

A car takes a flat curve of radius 120 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 = 120 mμs = 0.8g = 9.81 m/s²
vmax = m/s
5.Hard
R = 9 mh = 45 m

A 5 kg cart is released from rest at a height of 45 m on a frictionless track and runs through a vertical loop of radius 9 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 = 5 kgh = 45 mR = 9 mg = 9.81 m/s²
Nbottom = N
6.Hard
r = 1.1 m8 m/svtop​ = ?

A 1.7 kg ball on a light string 1.1 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 = 1.7 kgr = 1.1 mvbottom = 8 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. ac = 1.48 m/s²
  2. 2. ac = 2.847 m/s²
  3. 3. vmax = 19.93 m/s
  4. 4. vmax = 30.69 m/s
  5. 5. Nbottom = 539.6 N
  6. 6. Ttop = 15.52 N

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