A playground merry$-$go$-$round has radius $2\mathrm{.}30$ mm and moment of inertia $2400$ kg$$m$2$kg$$m$2$ about a vertical axle through its center, and it turns with negligible friction. A child applies an $24\mathrm{.}0$ NN force tangentially to the edge of the merry$-$go$-$round for $24\mathrm{.}0$ ss$.$ If the merry$-$go$-$round is initially at rest, what is its angular speed after this $24\mathrm{.}0$ ss interval? How much work did the child do on the merry go round?