A $84\mathrm{.}7$ kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of $1\mathrm{.}71$ rad$/$s$.$ A monkey drops a $9\mathrm{.}95$ kg bunch of bananas vertically onto the platform. They hit the platform at $4/5$ of its radius from the center, adhere to it there, and continue to rotate with it$.$ Then the monkey, with a mass of $21\mathrm{.}3$ kg$,$ drops vertically to the edge of the platform, grasps it$,$ and continues to rolate with the platform. Model the platform as a disk of radius $1\mathrm{.}81$ m$.$ Find the angular speed of the platform with its load. w$=$ mils