A $5\mathrm{.}5$ m diameter merry$-$go$-$round is rotating freely with an angular velocity of $0\mathrm{.}80$ rad$/$s$.$ Its total moment of inertia is $1,900$ kg$.$m$2.$ Four people standing on the ground, each with a mass of $80$ kg step on to the edge of the merry go$-$round.$$ What is the angular velocity of the merry$-$go$-$round after the fourth person steps on to it$?$ Provide you answer in radians per second.