Problem $6\mathrm{.}13($Rotating wheel$)$:

Consider a wheel rotating at constant angular velocity $.$ The hub and rim are assumed to be rigid $($non$-$deformable$).$ The spokes are cylinders each of cross$-$section $S,$ made up of an elastic material Young's modulus $E,$ mass density $).$ The spokes are assumed to work exclusively in tension or compression. There are $n$ such spokes, regularly spaced, Figure $6\mathrm{.}13.$ Determine the normal force $N$ in each spoke.

$**$PLEASE READ$**$ : The normal force in each of the bars comes from the reaction from the inner wheel, the outer wheel, and the distributed load because of the rotation. So$,$ when you cut a bar thus creating normal and shear $(=0)$ forces as well as a moment $(=0),$ you will have, as usual, the choice to consider the right side or the left side of the cut. You should provide the normal force at x$=$a as well as at x$=$b and plot the evolution of N$.$