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Rotation : Unolling carpet.

  1. Feb 14, 2012 #1
    1. The problem statement, all variables and given/known data
    A carpet of mass M made of in-extensible material is rolled along its length in the form of a cylinder of radius R an is kept on a rough floor. The carpet starts unrolling without sliding on the floor when a negligible small push is given to it. Calculate the horizontal velocity of the axis of the cylindrical part of the carpet when its radius reduces to R/2


    3. The attempt at a solution

    I tried conserving energy since friction wont be doing any work, my answer came out to be √(4gR/3)

    The answer in the book is √(14gR/3). Is anyone getting this answer?

    (Also, will angular momentum be conserved? I'm thinking yes.)
     
  2. jcsd
  3. Feb 14, 2012 #2

    tiny-tim

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    Hi AlchemistK! :wink:
    Yup!

    Show us what you did. :smile:
     
  4. Feb 14, 2012 #3
    Hint: Careful with kinetic energy considerations.
     
  5. Feb 15, 2012 #4
    x.x I got the answer, I made the mistake of assuming that since the radius dropped by half, even the mass dropped by half, while in fact it drops by a factor of 4.
    Thanks for your help! I'd never have even tried it again if didn't get to know that the answer was correct.
     
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