My Cherokee recently started making a whining sound when I start it up and when I accelerate (Video below). It mostly happens when it's cold outside. Once the engine warms up it stops. Everything handles as normal, haven't noticed any difference besides the sound. Recently got a new battery and starter. I replaced the serpentine belt and tension pulley about 2 years ago. The belt and all the pulleys look good to me.

The sound is clearly coming from the alternator. I've had alternators go out before, but never heard a sound like this. Is it going bad? I have the V6 so with all the extra space in the engine compartment it would be a very easy fix. But if I don't have to drop the money I dont' want too.

Ideas? Do I need a new alternator?

Here's the sound it makes:

 

Sounds like an $8 shaft bearing. You can replace it yourself, or buy a new alternator. Your choice.