A wheel is rotating about the fixed central axis with angular velocity $\backslash$omega i $=20$ rad$/$s$.$ Its

rotational inertia about the axis is$,$ I $=2$x$10-3$ kg m$2$

$.$ Due to frictional torque the wheel slows

down with angular deceleration, $\backslash$alpha $=-2\mathrm{.}5$ rad$/$s$2$ and stops, $\backslash$omega f $=0)($a$)$ Find the time to stop for

the wheel. What is the initial rotational kinetic energy of the wheel? $($b$)$ Find the magnitude of

the frictional torque acting on the wheel. What is time rate of change of the angular

momentum of the wheel?