Create a second layer and use it as a track matte.
This sort of basic stuff is covered in this resource: Getting started with After Effects That's the fastest free way to get up to speed with AE that I know.
Thanks for the info!
I read up on it, but I dont think this is what I am after. I do not want to show layers beneath anything, I would only like the animation to appear at a certain point in the rotation. In this picture below, I have highlighted where I do not want to see the circles in the middle of its rotation. Is there no way to mask this area of the circles to say "do not appear in this rectangle"?
There are 3 layers - the text is on one layer, the red circles are on a layer, and the grey are on the third layer.
Create a solid that is the shape of your red box. Pre-compose both of your circle layers. Put that solid above the pre-comp layer with the animated circles. Choose alpha inverted track matte has the option for the layer with the circles. Done.