Find Angular Velocity

Question

A uniform 2 kg solid disk of radius R = 0.4 m is free to rotate on a frictionless horizontal axle through its center. The disk is initially at rest, and then a 10 g bullet traveling at 510 m/s is fired into it as shown in the figure below. If the bullet embeds itself in the disk at a vertical distance of 0.2 m above the axle, what will be the angular velocity of the disk?

Here is the link to the image: https://freeimage.host/i/mW8quf

Answer 1

Just before impact, the total angular momentum is that of the bullet:

r × mv = (0,r,0) × m(v,0,0) = (0,0,–mrv).

After impact the total angular momentum is that of the rotating bullet-disk composite:

(I + i)ω = (MR ²/2 + mr ²)(0,0,–ω).

I think you can take it from here!