Nick,
Newton's 2nd Law of Motion
As the velocity is increased, then a force is generated tangentially in the direction of the velocity.
As the velocity is decreased, then a force is generated tangentially in the direction opposite to the velocity.
If the acceleration is proportional to the angular position, then you end up with a variation of Harmonic Motion.
Draw tangential force lines around a circle maximum length at the bottom reducing poportionally as you approach the top, reversing directions and increasing back to the bottom. You will now see that summed around the circle there is a net force. With two running counter to each other, you will see that all lateral forces are cancelled out.
If you can disprove this mathematically then please do.
Now, the problem is that the diagram does not have the whole system bounded. Where does the torque come from that accelerates and decelerates the masses? and how is it decoupled from the body of the inertia machine (so preventing Newton's third law) which would cancel out any effect.
I have asked Jiff how he intends to do this. What he has drawn so far is basic mechanics. I'm interested to see the torque generation system that is none Newtonian, if he has an answer to that then that would be something worth seeing.