Compulsory Problem$2$:

The uniform selender rod $AB$ with a mass of $5kg$ is attached to the wall by cable $CD$ and was realesed from rest at the position shown. The roller at $A,$ which has a negligible mass, is free to move along the frictionless horizontal surface.

As a first step to determine the angular acceleration of the rod$({}_{AB})$ and the tension in the cable $($T$)$ immeditely after the realese, kinematic analysis need to be done to write the acceleration of the center of mass of the $(vec(a{)}_G)$ ir terms of its angular acceleration. Assuming cew direction for ${}_{AB},$ we will find that

vec$(a{)}_G={}_{AB}$hat$()+0\mathrm{.}75{}_{AB}$hat$()$

Using the above result, determine:

$(1)$ the angular acceleration of the rod$({}_{AB})$

$(2)$ the tension in the cable $(T)$

$(3)$ the normal force at roller $A$