Solve it if you can

Classical Mechanics Level pending
  • 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 \(\lfloor x \rfloor \).

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