Does huge rotating AWACS radar affect flight characteristics? I would think that having a huge mass spinning around should produce massive gyroscopic forces when turning or pitching.
There must be some clever way of minimising or eliminating the effects... How is it done?  

(An example of the sort of thing I am talking about)
On the E2 Hawkeye the dish does not rotate very fast (ie, very slowly), and so the torque is probably negligible.  Usually the radomes are designed to help generate lift, and while certainly not as effective as a wing, do offset their own weight quite a bit.