In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it$.$ The diameter of the roller is $3\mathrm{.}00$ m$,$ and, while being driven into rotation around a fixed axis, its angular position is expressed as $=2\mathrm{.}00$t$20\mathrm{.}250$t$3$where is in radians and t is in seconds.$($a$)$ Find the maximum angular speed of the roller. rad$/$s$($b$)$ What is the maximum tangential speed of a point on the rim of the roller? m$/$s$($c$)$ At what time t should the driving force be removed from the roller so that the roller does not reverse its direction of rotation? s$($d$)$ Through how many rotations has the roller turned between t $=0$ and the time found in part $($c$)?$ rotations