Rolling The Distance

Classical Mechanics Level 3

A disk of mass M M , radius R R and linear velocity (of center of mass) = v c m v_{cm} is rolling without slipping on a rough ground with coefficient of friction μ \mu .

Calculate the distance covered by it (in meters) in one revolution.

Details and Assumptions

  • M = 3 k g M=3kg
  • R = 2 m R=2m
  • v c m = 4 m / s v_{cm}=4m/s
  • μ = 0.5 \mu=0.5


The answer is 16.

Ishan Singh by Ishan Singh , 22, India

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1 solution

Pinak Wadikar
Apr 29, 2014

I think Ishan wants to know the distance covered by bottom most point.

It's path will form a cycloid whose measure for 1 rotation is

8 × R = 8 × ( 2 ) 8 \times R = 8 \times (2)

Thus total distance covered = 16 \boxed{16}

NOTE: Such a problem is already present on Brilliant. Infact, I took the formula from the same problem.

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