# 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 "$${ u }_{ rel }$$" with respect to disc.

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

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

$\\ { \theta }_{ disc }\quad =\quad \pi \quad -\quad \pi \quad \times \sqrt { \cfrac { a }{ b } }$.

Then Compute " a + b " ?

Details

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

$$\bullet$$ Man moves on circumference of disc only.

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