A $4\mathrm{.}0$ m diameter merry$-$go$-$round is rotating freely with an angular velocity of $0\mathrm{.}50$ rad$/$s$.$ Its total moment of inertia is $1550$ kg $$ m$2.$ Four people standing on the ground, each of $65$ kg mass, suddenly step onto the edge of the merry$-$go$-$round.

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

$=$ rad$/$s

$($b$)$ Assume that the people were on it initially $(=0\mathrm{.}50$ rad$/$s$)$ and then jumped off in a radial direction $($relative to the merry$-$go$-$round$).$ What would be the angular velocity of the merry$-$go$-$round?

$=$ rad$/$s