A $3\mathrm{.}4-$m$-$diameter merry$-$go$-$round with rotational inertia $110$kg$$m$2$kg$$m$2$is spinning freely at $0\mathrm{.}60$rev$/$srev$/$s$.$ Four $25-$kg children sit suddenly on the edge of the merry$-$go$-$round.