The recoil you have on a normal weapon occurs as the mass you are projecting (i.e. bullet) is sped up. I would guess that the recoil in this weapon also happens as the mass is sped up. As the disc begins rotating, the force pushing back against the direction of rotation is equivalent of the force pushing back against the gun when it is fired. If the rounds were dropped into the disc after rotation has already started, the disc would experience a force opposite to its direction of rotation for each added round. This is the equivalent of recoil.
The problem with a weapon of this sort is that it has a large rotational momentum. If you tried to fire it while driving over bumps which change the axis of rotation, the top of the vehicle could be ripped entirely off if the system were not well reinforced.
This is a very revolutionary weapon. Ammunition would be lighter and cheaper because explosives would be unnecessary. The electrical power source is already built into many tanks. Accuracy is better without recoil and the speed at which mass is projected is simply incredible. One of the best advantages is that you have immediate 360 degree coverage because the ammunition can be released programmatically at any point in rotation. This means that you could give 4 gunners 4 scopes and have them all fire at a degree of rotation using the same weapon.
On a positive note, if you were driving under the influence, the cop behind you would never see you weaving down the road. 'Course, otoh, you might not be able to make any right turns either, and you could never go home again! ;-)