A student sits on a freely rotating stool holding two dumbbells, each of mass $2\mathrm{.}99$ kg $($see figure below$).$ When his arms are extended horizontally $($Figure a$),$ the dumbbells are $0\mathrm{.}99$ m from the axis of rotation and the student rotates with an angular speed of $0\mathrm{.}748ra\frac{d}{s}.$ The moment of inertia of the student plus stool is $2\mathrm{.}53kg*m^2$ and is assumed to be constant. The student pulls the dumbells inward horizontally to a position $0\mathrm{.}308$ m from the rotation axis $($Figure b$).$

$($a$)$ Find the new angular speed of the student.

rad$/$s

$($b$)$ Find the kinetic energy of the rotating system before and after he pulls the dumbbells inward.

$K_{\text{b}\text{e}\text{f}\text{o}\text{r}\text{e}}=$

$K_{\text{a}\text{f}\text{t}\text{e}\text{r}}=$

$J$