A dad pushes tangentially on a small hand$-$driven merry$-$go$-$round and is able to accelerate it from rest to a frequency of $14$ rpmrpm in $12\mathrm{.}0$ ss $.$ Assume the merry$-$go$-$round is a uniform disk of radius $2\mathrm{.}5$ mm and has a mass of $560$ kgkg$,$ and two children $($each with a mass of $25$ kgkg$)$ sit opposite each other on the edge.