Man moving on the disc!

Let a uniform circular disc of mass m and radius R is free to rotate in Horizontal Plane about a Point "O" at the edge ( Hinge at the Point "O" ) . A Man Having Same Mass m is standing at the point "A" which is just opposite diametric end point with respect to point "O" .


Now at time t=0 , man Starts moving with Constant velocity "urel{ u }_{ rel }" with respect to disc.

Then Find The angular displacement of the disc (θdisc{ \theta }_{ disc } ) in the time interval when Man reaches again at point "A" at the disc.

If Your answer is θdisc{ \theta }_{ disc } and it is expressed as :

θdisc=ππ×ab\\ { \theta }_{ disc }\quad =\quad \pi \quad -\quad \pi \quad \times \sqrt { \cfrac { a }{ b } } .

Then Compute " a + b " ?


Details

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

\bullet Man moves on circumference of disc only.


Original
This is part of my set Deepanshu's Mechanics Blasts
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