$4.$ A motor produces a time$-$dependent torque to spin up a flywheel. The torque is given by $($t$)=20$ t Nms$.$ The flywheel is a cylindrical disk of mass $10$kg and radius $0\mathrm{.}2$m$.$ If it starts from rest, how long will it take to be rotating at $1000$rad$/$s$?$ By how much angle will the flywheel have rotated once it has reached that speed from rest? Lastly, make plots of angular acceleration versus time, and angular velocity vs time.