The uniform rod $($length $0\mathrm{.}447$ m $)$ in the figure rotates in the plane of the figure about an axis through one end, with a rotational inertia of $0\mathrm{.}175kg*m^2.$ As the rod swings through its lowest position, it collides with a $0\mathrm{.}258$ kg putty wad that sticks to the end of the rod. If the rod's angular speed just before the collision is $1\mathrm{.}02ra\frac{d}{s},$ what is the angular speed of the rod$-$putty system immediately after the collision?

Number Units