In the diagram, disk $1$ has a moment of inertia of $4\mathrm{.}2kg*m^2$ and is rotating in the counterclockwise direction with an angular velocity of $7\mathrm{.}3$ rad$/$s about a frictionless rod passing through its center. A second disk rotating clockwise with an angular velocity of $8\mathrm{.}9ra\frac{d}{s}$ falls from above onto disk $1.$ The two then rotate as one in the clockwise direction with an angular velocity of $2\mathrm{.}6ra\frac{d}{s}.$ Determine the moment of inertia, in $kg*m^2,$ of disk $2.$

$kg*m^2$