$(12$ pts$.)$ A rotating disk accelerates uniformly from $300\mathrm{.}0re\frac{v}{m}in$ to $1\mathrm{.}50{10}^3$ rev$/$min in $5\mathrm{.}00$ s $.$

a$)$ What is the $($constant$)$ angular acceleration of the disk $($in $ra{d}^2{s}^2)?$

b$)$ How many revolutions did the disk make during the five seconds?