$10\mathrm{.}18$ A $10$ kg disk with a radius of $20$ cm spins on an axis through its center at an angular velocity of $320$ rad$/$s$.$ a$)$ What torque must be applied to bring the disk to rest over a time interval of $45$ s$?$ b$)$ Through what angle does the disk turn in $45$ s$?$ c$)$ What is the initial kinetic energy of the disk? d$)$ Use W $=$ $$ to test the work$-$kinetic energy theorem.