Conservation of Angular Momentum in a Rotating System

[physics123456]

Homework Statement

A circular turntable of mass 2.0 kg and radius 6.0 inches is rotating freely at 66 2/3 rpm. If a 500 gram blob of clay is dropped on the disk at a distance of 4.0 inches from the center, what is the resulting angular speed of the system? Treat the clay as a point mass (I = MR^2) and the turntable as a disk.

Homework Equations

The Attempt at a Solution

I understand the resulting angular speed will be the sum of the two. But what does moment of inertia have to do with it??

 

[haruspex]

What do you mean about the angular speed being the sum of the two? Doesn't sound right.
What relevant conservation law do you know?