A square plate with sides $2\mathrm{.}3$ m in length can rotate around an axle passing through its center of mass $($CM$)$ and perpendicular to its surface $($see figure below$).$ There are four forces acting on the plate at different points. The rotational inertia of the plate is $33kg*m^2.$ Use the values given in the figure to answer the following questions. Assume the plate starts from rest. $($Assume $=55.)$

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$($a$)$ What is the angular velocity of the plate after $4\mathrm{.}0$ s $?($Express your answer in vector form.$)$

vec$()=ra\frac{d}{s}$

$($b$)$ Through how many revolutions will the plate rotate in $4\mathrm{.}0$ s $?$

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