$4\mathrm{.}2-$m$-$diameter merry$-$go$-$round is rotating freely

with an angular velocity of Its total moment

of inertia is Four people standing on the

ground, each of mass $65$ kg$,$ suddenly step onto the edge

of the merry$-$go$-$round. $($a$)$ What is the angular velocity of

the merry$-$go$-$round now? $($b$)$ What if the people were on it

initially and then jumped off in a radial direction $($relative

to the merry$-$go$-$round$)?$