$(14$ pts$)$ A merry$-$go$-$round is a solid cylinder platform with the mass

M$=100$kg$,$ radius r$=1\mathrm{.}50$m$,$ and a frictionless axle at the center. Two students

with masses m$\_(1)=70\mathrm{.}0$kg and m$\_(2)=65\mathrm{.}0$kg are standing at the rim of the

platform. The platform is initially at rest. A third student, standing on the

ground, applies a constant force tangential to the rim, spinning it up with an

angular acceleration of $0\mathrm{.}450$ra$($d$)/($s$^(2)).($e$)(4$ pts$)$ The two students on the platform move towards the center of the platform. What is the angular speed of the platform when they are at the center?