Problem #$2$: $(35$ points$)$ A uniform bar ACB of mass $m=5kg$ and length $L=1\mathrm{.}2m$ is pinned at $-$

and rotates about $-$ point $C.$ The distance from the fixed point $C$ to the center of mass $G$ of the bar

is $\frac{?}{\text{b}\text{a}\text{r}}(r)=0\mathrm{.}30m.$ At the instant depicted in the vertical plane shown in Figure $2,$ the bar is in the

vertical position shown rotating with a clockwise angular velocity ${}_{\text{A}\text{C}\text{B}}=5ra\frac{d}{s}$ when it is

suddenly subjected to a horizontal force $P=100N$ at end $B,$ as shown.

a$)$ Calculate the moment of inertia $I_C$ of bar ACB about point $C.$

b$)$ Calculate $-$ at the instant immediately before the force $P$ is first applied $-$ the reactions at pin

$C,$ the angular acceleration ${}_{\text{A}\text{C}\text{B}}$ of bar ACB, and the $x-$ and $y-$components $(a_G{)}_x$ and $(a_G{)}_y$ of

the acceleration the center of mass $G$ of bar ACB.

c$)$ Calculate $-$ at the instant immediately after the force $P$ is first applied $-$ the reactions at pin

$C,$ the angular acceleration ${}_{\text{A}\text{C}\text{B}}$ of bar ACB, and the $x-$ and $y-$components $(a_G{)}_x$ and $(a_G{)}_y$ of

the acceleration the center of mass $G$ of bar ACB.