A man of mass \( m_{1} \) stands on the edge of a horizontal uniform disc of mass \( m_{2} \) an...

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A man of mass \( m_{1} \) stands on the edge of a horizontal uniform disc of mass \( m_{2} \) and radius \( R \) which is capable of rotating freely about a stationary vertical axis passing through its centre. At a certain moment the man starts moving along the edge of the disc; he shifts over an angle \( \phi^{\prime} \) relative to the disc and then stops. In the process of motion the velocity of the man varies with time as \( v^{\prime}(t) \). Assuming the dimensions of the man to be negligible, find:
the force moment (relative to the rotation axis) with which the man acted on the disc in the process of motion.
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