A $81\mathrm{.}3kg$ horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of $1\mathrm{.}57ra\frac{d}{s}.$

A monkey drops a $9\mathrm{.}21kg$ bunch of bananas vertically onto the platform. They hit the platform at $\frac{4}{5}$ of its radius from the

center, adhere to it there, and continue to rotate with it$.$ Then the monkey, with a mass of $21\mathrm{.}9kg,$ drops vertically to the edge of

the platform, grasps it$,$ and continues to rotate with the platform.

Model the platform as a disk of radius $1\mathrm{.}51m.$