Problem $15$: $(6\backslash \%$ of Assignment Value$)$

A thin rod with a mass of $3\mathrm{.}09$ kg and a length of $46\mathrm{.}2$ cm is free to rotate in the $\backslash ($ x$-$y $\backslash )$ plane and about the $\backslash ($ z $\backslash )$ axis, which

passes through its center. Initially at rest, a constant torque, $\backslash (\backslash$vec$\{\backslash$tau$\}=(19\mathrm{.}5\backslash$mathrm$\{$mN$\}\backslash$cdot $\backslash$mathrm$\{$m$\})\backslash$hat$\{$k$\}\backslash ),$ is applied.

In lieu of the typical table as found in most textbooks, the MOIs of uniform standard objects may be obtained by using the left and right arrows to step through the image carousel to the right.

Part $($a$)$

How much time, in seconds, elapses before the thin rod achieves an angular velocity of $24$ rpm $($revolutions per minute.$)?$

$\backslash [$

$\backslash$Delta t$=\backslash$mid

$\backslash ]$