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 = ?300 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 2 m/s². What is the smallest radius rmin for a curve taken at 300 km/h?

v = 300 km/hamax = 2 m/s²
rmin = m
2.Easy
r = 190 m29 m/sF = ?

A 1000 kg car drives around a flat curve of radius 190 m at a constant 29 m/s. Find the inward (centripetal) force Fc needed.

m = 1000 kgv = 29 m/sr = 190 m
Fc = N
3.Medium
r = 130 mvmax​ = ?

A car takes a flat curve of radius 130 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 130 mμs = 0.6g = 9.81 m/s²
vmax = m/s
4.Medium
L = 1.3 m15°

A small ball on a string of length 1.3 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 = 1.3 mθ = 15°g = 9.81 m/s²
v = m/s
5.Hard
r = 1 mv = 6.5 m/s

A 1.4 kg ball on a string 1 m long is swung in a vertical circle. At the lowest point it moves at 6.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.4 kgr = 1 mv = 6.5 m/sg = 9.81 m/s²
T = N
6.Hard
R = 2.5 mh = 8 m

A 2 kg cart is released from rest at a height of 8 m on a frictionless track and runs through a vertical loop of radius 2.5 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 = 2 kgh = 8 mR = 2.5 mg = 9.81 m/s²
Nbottom = N

Answer key

  1. 1. rmin = 3472 m
  2. 2. Fc = 4426 N
  3. 3. vmax = 27.66 m/s
  4. 4. v = 0.9404 m/s
  5. 5. T = 72.88 N
  6. 6. Nbottom = 145.2 N

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