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## Homework Statement

Hi there. I have some doubts about an example I've found on the Ingard book of mechanics, matter and waves.

It says:

*It is given to a homogeneous cylinder a horizontal speed V1 and an angular speed in opposed sense to that of the needles of the clock [tex]\omega_1=\frac{V_1}{R}[/tex] in the exempt part of frictions of a horizontal surface. But there of the point A, it changes the surface so that to the right of A the friction coefficient it is [tex]\mu[/tex]*

Once it has happened of A the cylinder, will slip firstly on the rough plan, but it will finish rotating without slipping. In that point when it began to rotate without slipping which will the speed corresponding of the center of mass be?

Once it has happened of A the cylinder, will slip firstly on the rough plan, but it will finish rotating without slipping. In that point when it began to rotate without slipping which will the speed corresponding of the center of mass be?

__The only force that it is exercised on the body in the address of the movement it's the contact force and in consequence, their action line is in the plane.__**Therefore, the angular moment of the cylinder regarding a point of reference of the plane, will remain constant during the whole movement.**I don't understand how its deduced that the angular momentum will be conservative respect a point over the plane. Could somebody help me to make this clear? The underline and the bold marks the principle and conclusion that I don't understand. How does it implies that the force is actioned over the plane the conservation of angular momentum?

Thanks!