Sam $(47\mathrm{.}37$ kg$)$ and Alex $(80\mathrm{.}8$ kg$)$ sit on opposite ends of a see$-$saw as shown in the figure.$$ Determine the angular acceleration $($rad$/$s$^2)$ of the see$-$saw if Sam sits $1\mathrm{.}33$ m and Alex sits $2\mathrm{.}45$ m from the pivot.$$ The see$-$saw board has a moment of inertia of $22\mathrm{.}0$ kgm$2$ about the pivot, and treat Sam & Alex as point masses at their distance from the center pivot to determine their moments of inertia $($I $=$ mk$2,$ where k $=$ distance from pivot$).$ Include a FBD as practice and to assist in your solution $($does not have to be submitted$).$

Consider$/$hint: why does the moment of force from the see$-$saw board not have to be considered but the board's moment of inertia does?

Consider$/$hint: if Alex wanted to increase acceleration of the see$-$saw, would it be better to increase his mass by $10\%$ or increase his distance from the pivot by $10\%?$

Consider$/$hint: how would variables $($Fg$,$ moment arms, moments of force, moments of inertia of Sam, Alex, the board, vertical force acting on the board from the pivot, angular acceleration$)$ change if $1)$ the distances of Sam & Alex were halved; $2)$ Sam & Alex swapped to the other side, either at their original or at the other's distance?