A solid rubber ball is at rest at the top of a wood incline $0\mathrm{.}2$ m up from the base. When released, it rolls without slipping. The ball hits the end of a stationary aluminum rod that is the same height as the center of the ball. The rod then rotates around a smooth, vertical, bearing at its center. The coefficient of restitution of aluminum on rubber is $e=0\mathrm{.}8.$ Determine the angular velocity of the rod and velocity of the center of the ball after the collision. The mass of the rod is $1\mathrm{.}1$ kg and its length is $1\mathrm{.}0$ m $.$ The mass of the ball is $0\mathrm{.}26$ kg and its radius is $0\mathrm{.}04$ m $.$