All Problems Dynamics of a solid body
Problem 1.277
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 \(\varphi^{\prime}\) relative to the disc and then stops. In the process of motion the velocity of the man varies with time as \(v^{\prime \prime}(t)\). Assuming the dimensions of the man to be negligible, find: (a) the angle through which the disc had turned by the moment the man stopped; (b) the force moment (relative to the rotation axis) with which the man acted on the disc in the process of motion.
(a) \(\varphi=-\frac{2 m_{1}}{2 m_{1}+m_{2}} \varphi^{\prime}\) (b) \(N_{z}=-\frac{m_{1} m_{2} R}{2 m_{1}+m_{2}} \frac{d v^{\prime}}{d t}\).