My space ship weapon

Hello all, First of all I’m new to this site and pretty new to Blender. This is my WIP of the gun I am building right now and I am confused on how to get the three gun barrels to rotate by them selves. I late plan to model out a space ship but I wanted to start with the guns first (something small before I jump in the deep end lol). Tell me what you think! And if possible can you help me figure out how to get the rotating on the Y axis animated?

I have been reading up on the Blender wiki about animation, rotation, parent and child. Still every time I go to animate the barrels the whole thing spins on the pivot point of the main object.