Angular velocity of sphere and two points

[KaiserBrandon]

Homework Statement

A uniform sphere of mass m and radius R rotates around the vertical axis with angular speed $$\omega$$. Two particles of mass m/2 are brought close to the sphere at diametrically opposite points, at an angle $$\Theta$$ from the vertical. The masses, which are initially essentially at rest, abruptly stick to the sphere. What angle does the resulting $$\vec{\omega}$$, make with the vertical?

Homework Equations

so the moment of inertia of the sphere by itself is $$I=\frac{2}{5}mR^{2}$$

The Attempt at a Solution

I don't really know how to start this question off, or what method I would use. There is a changing moment of inertia, so would I use conservation of angular momentum to find the resulting angular velocity?

 

[RoyalCat]

Yes, that's exactly right. Why not try and solve it and show us if you get stuck at any point along the way?

As a general note, we won't do your homework for you here, you should show your own attempt at the solution in order for us to help you the best we can.