# 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.