A $3\mathrm{.}5-$m$-$diameter merry$-$go$-$round with rotational inertia $100$ kg$$m$2$kg$$m$2$ is spinning freely at $0\mathrm{.}40$ rev$/$srev$/$s $.$ Four $25-$kg children sit suddenly on the edge of the merry$-$go$-$round.Find the new angular speed.Determine the total energy lost to friction between the children and the merry$-$go$-$round.