$3.$ A $2-$kg mass rests on a flat horizontal bar. The bar begins rotating in the vertical plane about O with a constant angular acceleration of $1$ rad$/$s$?.$ The mass starts to slip on the bar when the bar is $45\backslash$deg above the horizontal. $(20$ pts$)($a$)$ Draw the free$-$body diagram. $(5$ pts$)($b$)$ What is the static coefficient of friction between the mass and the bar?.$(10$ pts$)($c$)$ Does the mass slip toward or away from O$?(5$ pts$)$

A $2-$kg mass rests on a flat horizontal bar. The bar begins rotating in the vertical plane about $O$ with a constant angular acceleration of $1ra\frac{d}{s^2}.$ The mass starts to slip on the bar when the bar is $45$ above the horizontal. $(20pts)$

$($a$)$ Draw the free$-$body diagram. $(5pts)$

$($b$)$ What is the static coefficient of friction between the mass and the bar?. $(10$ pts$)$

$($c$)$ Does the mass slip toward or away from O $?(5$ pts$)$