Problem $2.$ A frictionless rod is rotating freely with an initial angular speed ${}_0$ about a vertical

axis. The two sliders, each of mass $m,$ are released at a radial distance $r=a.$ The rod is massless.

The stops at the ends of the rod each have a mass $\frac{m}{2}.$

a$.$ Find the angular speed of the system after the sliders come to rest at the stops.

b$.$ Find and explain the change in kinetic energy of the system.