A student sits on a rotating stool holding two $2\mathrm{.}5-$kg objects. When his arms are extended horizontally, the objects are $1\mathrm{.}0$ m from the axis of rotation and he rotates with an angular speed of $0\mathrm{.}75$ rad$/$s$.$ The moment of inertia of the student plus stool is

$3\mathrm{.}0$ kg $$ m$2$

and is assumed to be constant. The student then pulls in the objects horizontally to $0\mathrm{.}47$ m from the rotation axis.

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

rad$/$s

$($b$)$ Find the kinetic energy of the student before and after the objects are pulled in$.$

before$$ Jafter$$ J