$(1$ point$)$ On a frictionless table, a $0\mathrm{.}62$ kg glob of clay strikes a uniform $1\mathrm{.}72$ kg bar perpendicularly at a point $0\mathrm{.}26$ m from the center of the bar and sticks to it$.$ If the bar is $0\mathrm{.}78$ m long and the clay is moving at $6\mathrm{.}80\frac{m}{s}$ before striking the bar, what is the final speed of the center of mass?

At what angular speed does the bar$/$clay system rotate about its center of mass after the impact?