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 = 50 m18 m/sF = ?

A 600 kg car drives around a flat curve of radius 50 m at a constant 18 m/s. Find the inward (centripetal) force Fc needed.

m = 600 kgv = 18 m/sr = 50 m
Fc = N
2.Easy
r = 80 m28 m/sF = ?

A 1500 kg car drives around a flat curve of radius 80 m at a constant 28 m/s. Find the inward (centripetal) force Fc needed.

m = 1500 kgv = 28 m/sr = 80 m
Fc = N
3.Medium
r = 65 mvmax​ = ?

A car takes a flat curve of radius 65 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 = 65 mμs = 0.3g = 9.81 m/s²
vmax = m/s
4.Medium
r = 95 mvmax​ = ?

A car drives over the top of a hump in the road, which is a circular arc of radius 95 m. Use g = 9.81 m/s². Above what speed vmax do the wheels leave the road at the top?

r = 95 mg = 9.81 m/s²
vmax = m/s
5.Hard
R = 7 mh = 27.3 m

A 2 kg cart is released from rest at a height of 27.3 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 Nbottom of the track on the cart at the bottom of the loop.

m = 2 kgh = 27.3 mR = 7 mg = 9.81 m/s²
Nbottom = N
6.Hard
r = 1.1 m8.5 m/svtop​ = ?

A 2 kg ball on a light string 1.1 m long is swung in a vertical circle. At the lowest point its speed is 8.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 2 kgr = 1.1 mvbottom = 8.5 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. Fc = 3888 N
  2. 2. Fc = 14700 N
  3. 3. vmax = 13.83 m/s
  4. 4. vmax = 30.53 m/s
  5. 5. Nbottom = 172.7 N
  6. 6. Ttop = 33.26 N

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