The bar OA rotates about a horizontal axis through O with a counterclockwise angular velocity $\backslash$omega $.$ As it passes the position

when $\backslash$theta $=0\backslash$deg a small block of $1-$lb weight is placed on the bar at a distance of $18$ inches from $0.$ When $\backslash$theta $=50\backslash$deg the angular

velocity is $\backslash$omega $=3$ rad$/$s and is increasing with a rate of $2$ rad$/$s$2.$ Also, the block starts to slip toward the hinge O$.$

a$.$ Draw a free$-$body diagram of the block when $\backslash$theta $=50\backslash$deg $,$ do not forget gravity

b$.$ Calculate the normal force exerted on the block by the bar OA$.$

c$.$ Calculate the coefficient of static friction

d$.$ Once the block starts to slide, the frictional force is governed by the coefficient of kinetic friction. Apply Newton$$s

$2$nd Law and formulate the equation of motion in the radial direction. You do not need to solve the equation.