A $4\mathrm{.}5-$mm$-$diameter merry$-$go$-$round is rotating freely with an angular velocity of $0\mathrm{.}70$ rad$/$srad$/$s $.$ Its total moment of inertia is $1340$ kg$$m$2$kg$$m$2.$ Four people standing on the ground, each of mass $63$ kgkg $,$ suddenly step onto the edge of the merry$-$go$-$round. What is the angular velocity of the merry$-$go$-$round now? What if the people were on it initially and then jumped off in a radial direction $($relative to the merry$-$go$-$round$)?$