Its a collosally impractical idea for many reasons, but I'll give the simplest one Whatever rotating mechanism (call it flywheel) they have needs to be charged

Its a collosally impractical idea for many reasons, but I'll give the simplest one Whatever rotating mechanism (call it flywheel) they have needs to be charged up with rotational energy to launch. The amount of energy remaining in it after the projectile gets launched is the fraction M/(M+m) where M is the flywheel mass and m is the mass of the projectile. Now you see the problem (if you have any physics instinct) If you dont want a sudden shift in the center of rotation (going off balance) then you need the flywheel mass to be high. But the higher the flywheel mass, the more amount of energy left "wasted" as it spins to a halt in the de-evacuated atmosphere. Bearings can handle some amount of jerking and some amount of imbalance in most applications. But here there is massive centrifugal pull of the imbalanced flywheel, the instantaneous jerk as the rotational center shifts after launch, shock wave of the instantaneous rushing in of air into the vacuum (speed of sound), the massive heating up of the whole structure, the precession that may be induced by turbulence etc. This will most likely destroy the whole shebang in seconds, if not make it completely unusable a second time. Slingshots work only because the sling has negligible mass compared to the stones that are launched. This comic book idea dreamed by by some non-engineer is just going to eat up investor money and lots of precision machined equipment