A $\backslash (500-\backslash$mathrm$\{$kg$\}\backslash )$ concrete culvert, shaped like a hollow cylinder with a mean radius of $0\mathrm{.}5$ m $($ignore its thickness$),$ is loaded on the back of a truck. The truck accelerates forward at $\backslash (3\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash ).$ Assuming the culvert rolls without slipping on the truck bed:

$1.$ Find the magnitude and direction of the angular acceleration of the culvert $(\backslash (\backslash$alpha $\backslash ))$

$2.$ Find the magnitude and direction of the tangential acceleration of the center of mass of the culvert