The $9-kg$ uniform slender bar $AB$ of length $l=1\mathrm{.}2m$ is pinned freely to the collar. The system is initially at rest in a horizontal plane with the bar in the position $=10$ when the collar starts moving with a constant acceleration $a=2\frac{m}{s^2}$ along the fixed rod. Consequently, the bar rotates about pin $A$ in the horizontal plane. $($a$)$ Determine the angular acceleration of the bar as a function of $.($b$)$ Determine the angular velocity of the bar as a function of $.($c$)$ Determine the total horizontal force supported by pin $A$ at the instant when $,A=27\mathrm{.}0N)$