When a $2\mathrm{.}75-$kg fan, having blades $18\mathrm{.}5$ cm long, is turned off, its angular speed decreases uniformly from $10\mathrm{.}0$ rad$/$s to $6\mathrm{.}30$ rad$/$s in $5\mathrm{.}00$ s$.$a$.$ What is the magnitude of the angular acceleration of the fan?b$.$ Through what angle $($in degrees$)$ does it turn while it is slowing down during the $5\mathrm{.}00$ s$?$c$.$ If its angular acceleration does not change, how long after it is turned off does it take the fan to stop.