The rolling starts now...

A uniform wheel(disc) of radius \( R \) was set rotating about its axis at an angular speed \( \omega \). Now it is carefully placed on a rough horizontal surface of friction coefficient \( \mu \) with its axis horizontal. Because of friction the wheel accelerates forward and its rotation decelerates till the wheel starts pure rolling. If the time after which pure rolling starts on the surface is given by \( \frac { a }{ b } \frac { R\omega }{ \mu g } \) then find \( a+b \).

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