How Does Collision Affect Angular Speed in Rotational Motion?

[uchicago2012]

Homework Statement

In the figure, a small particle of mass m = 25 grams moving at speed of v0 = 12 m/s sticks to the edge of a disk of mass M = 500 grams and radius = 11 cm. The disk then rotates freely about its axis as a result of the collision. (The disk is on an axle.) Find the angular speed after the collision.
See Figure 1

The Attempt at a Solution

can I break up a moment of inertia and add its parts?
I = I_disk + I_particle

 

[quenderin]

Yes, moments of inertia add. It is after all an integral of the form

$$\int r^2 \, dm$$

so you're free to break up an object into chunks, find the moment of inertia of each part and then sum them up altogether in the end.