Solve it if you can

• A man of mass $M$ stands at point $A$ on a horizontal lamina which is free to rotate about a fixed point $O$ . Initially both are at rest.The man then walks along the circle with $OA$ as diameter ( $OA=a$ ). Returning to his starting point.

$I$ is moment of inertia of lamina about $O$ .

If the angle turned is $x$ times the value in picture, find $\lfloor x \rfloor$ .