Homework Help: Rotation : Unolling carpet.

1. Feb 14, 2012

AlchemistK

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. Feb 14, 2012

tiny-tim

Hi AlchemistK!
Yup!

Show us what you did.

3. Feb 14, 2012

LawrenceC

Hint: Careful with kinetic energy considerations.

4. Feb 15, 2012

AlchemistK

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.