Variable friction on the Horizontal disc

Classical Mechanics Level 4

A uniform disc is rotating with angular velocity $\omega$ and then it is gently placed horizontally on a rough horizontal surface having a coefficient of friction $\mu$ . The total time $T$ taken by disc to stop rotating completely can be expressed as

$T\quad =\cfrac { a }{ b } \times \cfrac { \omega R }{ \mu g }$ .

Find The value of $a\times b$ .

Details:

$\bullet$ 'a' and 'b' are Co-prime positive integers.

Variable friction on the Horizontal disc

This was asked by my friend Lakshya Kumar