A $8\mathrm{.}90-$m ladder with a mass of $22\mathrm{.}2$ kg lies flat on the ground. A painter grabs the top end of the ladder and pulls straight upward with a force of $264$ N$.$ At the instant the top of the ladder leaves the ground, the ladder experiences an angular acceleration of $2\mathrm{.}00$ rad$/$s~ about an axis passing through the bottom end of the ladder. The ladder's center of gravity lies halfway between the top and bottom ends. $($a$)$ What is the net torque acting on the ladder? $($b$)$ What is the ladder's moment of inertia?