Problem 1.187

A disc $A$ of mass $m$ sliding over a smooth horizontal surface with velocity $v$ experiences a perfectly elastic collision with a smooth stationary wall at a point $\hat{O}$ (Fig. 1.48$) .$ The angle between the motion direction of the disc and the normal of the wall is equal to $\alpha .$ Find: (a) the points relative to which the angular momentum M of the disc remains constant in this process; (b) the magnitude of the increment of the vector of the disc's angular momentum relative to the point $O^{\prime}$ which is located in the plane of the disc's motion at the distance $l$ from the point $O$