XERCICE $3$: $13$ points $+2$ bonus points

Let a sliding pivot link of axis & with play between a shaft of mass $M$ and a boring. The shaft has a rotation speed of $w,$ non$-$zero and a zern on

During the operation of this link, the friction of coefficient $u$ or the adhesion of coefficient $\text{'}$ exists. It is assumed that the contact surface between the axis and the bore is the lower half$-$cylinder $($half$-$cylinder under the axis of symmetry$).$ The objective of the exercise is to determine the static torsor of the bond in the state described here.

Specify and justify whether the phenomenon is friction or adhesion?

Inventory all the forces of the bore acting on the rod and draw them on the drawing and on a view at the end. Place the axes necessary to solve the problem.

Evaluate the static torsor of the link from the data of the previous question $($do not make any assumption here about the distribution of local contact pressures$)$

Continue the previous calculation using a distribution of local uniform contact pressures. Express according to $M,g,H^{\text{'}},M,$ and r $.$

The previous hypothesis $($local contact pressures with respect to the contact surface$)$ is not mechanically realistic. Change the assumptions to become more realistic.

A$.$ Explain your hypothesis and define the expression of the distribution of local contact pressures.

B$.$ Redo the calculation.