Question $2(15$ points$)$

In the following figure, a man is pushing a merry$-$go$-$round with a force of $250$ N $.$ The merry$-$go$-$round has a mass of $50$ kg and a radius of $1\mathrm{.}5$ m $.$

a$)$ Using Inertia Method, calculate the angular acceleration produced when no one is on the merry$-$go$-$round. Consider the merry$-$go$-$round itself to be a uniform disc with negligible retarding friction. $($Blank $1)$

b$)$ How long does it take the man to give the merry$-$go$-$round an angular velocity of $1\mathrm{.}50$ rad$/$s$?($Blank $2)$

c$)$ How many revolutions must he go through to generate this velocity? $($Blank $3)$

Blank $\backslash$# $1$

Blank $\backslash$# $2$ A$)$

Blank $\backslash$# $3$ A