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.