A playground merry$-$go$-$round has radius $2\mathrm{.}20$ 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 $23\mathrm{.}5$ NN force tangentially to the edge of the merry$-$go$-$round for $25\mathrm{.}0$ ss$.$ If the merry$-$go$-$round is initially at rest, what is its angular speed after this $25\mathrm{.}0$ ss interval?

Express your answer in radians per second.

How much work did the child do on the merry$-$go$-$round?

Express your answer in joules.

What is the average power supplied by the child?

Express your answer in watts.