Finding moment of inertia when two rotating disks combine

[Mia]

Homework Statement

In the diagram, Disk 1 has a moment of inertia of 4.40 kg · m2 and is rotating in the counterclockwise direction with an angular speed of 7.50 rad/s about a frictionless rod passing through its center. A second disk rotating clockwise with an angular speed of 9.50 rad/s falls from above onto Disk 1. The two then rotate as one in the clockwise direction with an angular speed of 1.40 rad/s. Determine the moment of inertia of Disk 2.

Homework Equations

L=Iω

The Attempt at a Solution

I have no idea how to start the problem.

 

[haruspex]

I have no idea how to start the problem.

Any conservation laws you can think of that might apply?