$]$ Two forces are applied to a system that contains two solid disks bolted to each other, which as a unit rotate around their central axis. The forces are given by $1=200\mathrm{.}0$ and $2=100\mathrm{.}0.$ The small disk has a radius of $1=0\mathrm{.}60,$ and the large disk has a radius of $2=1\mathrm{.}0.$ Each disk has a mass of $20\mathrm{.}0.$ a$)$ What is the total moment of inertia of the system? b$)$ What is the angular acceleration of the system? c$)$ If the system starts at rest, and the forces are applied continuously, how many revolutions do the disks make after $23$ have elapsed?