Question

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 $O$ (figure shown above). The angle between the motion direction of the disc $A$ and the normal of the wall is equal to $\alpha$. Find 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 $O$.

• A. $|\Delta m|=3mvl\cos \alpha$
• B. $|\Delta m|=mvl\cos \alpha$
• C. $|\Delta m|=2mvl\cos \alpha$
• D. $|\Delta m|=4mvl\cos \alpha$

Answer 1

The correct option is C $|\Delta m|=2mvl\cos \alpha$

Initial Angular momentum is $Mvlsin(90-\alpha )$ not just Mvl because l is not the perpendicular distance between the line of impact and the point.
therefore
Initial AM $=-Mvlsin(90-\alpha )$
Final AM $=Mvlsin(90-\alpha )$
Increment $=2MvlCos\left(\alpha \right)$