Fraction of energy dissipated when solid cylinder placed on table

[looli9]

A uniform solid cylinder is set spinning about its axis and is then gently placed, with the axis horizontal, on a rough horizontal table. What fraction of its initial kinetic energy is dissipated in sliding friction before the cylinder eventually rolls smoothly along the plane?

The only equations I think are needed are 0.5mv^2 and 0.5Iw^2, and I can write down equations for the total energy before and after, but cannot relate the two.

Apparently the answer is 2/3.

Thanks

 

[arildno]

Think conservation of angular momentum with respect to the point of contact.