$3)$ In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it$.$ The diameter of the roller is $2\mathrm{.}00$ m$,$ and, while being driven into rotation around a fixed axis, its angular position is expressed as $=2\mathrm{.}90$t$20\mathrm{.}900$t$3$

where $$ is in radians and t is in seconds.

$($a$)$ Find the maximum angular speed of the roller.

$($b$)$ What is the maximum tangential speed of a point on the rim of the roller?