The Paradox Engine

[Tusk]

I may have this wrong, which is why I am bringing it up.

Ok webby1 I'll try to retrace your steps and point to any differences between my interpretation and your own.

If the disc is not allowed to rotate about its center of mass and the arm were to make one rotation then the arm would see the disc make one rotation, and the disc would see the arm make one rotation.

This first set of conditions is a little unclear; if you mean that the disk is prevented by inertia from rotating as the rotor arm rotates then yes, the observation is correct.

To have the arm make one rotation and have the disc make one rotation about is center of mass while it is orbiting the pivot for the arm, the arm would see the disc make 2 rotations and the disc would see the arm make 2 rotations.

Again, based on my interpretation of your first premise this is correct for one direction of rotation but not the other; reverse motion to the opposite you had in mind and each would see the other as motionless (which point actually lends a little more clarity).

From the PoV of the applied force of acceleration against the disc, the edge of the disc will move twice as far as the arm.

Correct.

I interpret this then that the disc is spun up with full force over twice the distance of reaction from the arm,

And this is where things get tricky; you seem clear on the point that the disk will receive 50% of it's rotation from inertia (due rotor arm motion) and unclear how to proceed regarding determination of work done since this relates to force applied over a distance, but our disk is covering twice as much distance with a 50% assist from inertia.

So here's the interesting part then, since it's no simple matter:

the arm having an equal force of motion but at 1\2 the distance and the disc is left with an increase in potential due to its rotation which when recovered will impart the full force into the arm over another 1\2 distance. 

My thoughts on this lately have me inclined to slow the rotation of the rotor arm using a geared output to a generator. This sidesteps these issues quite tidily 

Your meaning on this last point is again a little unclear, but if you are defining the motion by distance (which you seem to be doing) then it sounds like it might be correct for the current single disk PE apparatus. Your method of resolving it differs from my own. Also note that everything changes with two disks and a lightweight rotor arm.

[Tusk]

Ok this inertial rotation of the disk seems to be causing some concern; let's add another line of code then, and demonstrate the potential to sidestep and maybe even use our opponent's weight against himself 

If we recover energy at the disk axis (i.e. a geared generator) no secondary reaction manifests and any retarding force on the rotor arm from the disk axis (due to resistance from the generator) is minimised. This gives us the option to recover energy from the disk without significantly reducing rotor arm motion.

Am I right in suggesting this? I'm off the reservation again here, so keep a close eye on things 

Additional: I assume this is so due to the disk axis being located at a large enough radius from the rotor arm axis that the (essentially) two opposing forces at the generator will have nearly equal moment arms (depending on the relative size/diameter of the generator with regard to the radius) while noting that some bias will manifest; and that against our purpose.

First glance at this suggests the possibility of 'spinning up' as per usual, then recovery of total rotor arm FoR disk energy at the disk axis (as above) without significant reduction of rotor arm motion. By this (bold print) I refer to the full disk rotation rate as it appears in the frame of reference of the rotor arm. As we already noted this can be as much as double the rotation rate in the observer FoR.

So having brought the disk to a stop (FoR rotor arm) we can now recover energy from the rotor arm, which will induce yet another rotation of the disk (FoR rotor arm) due to inertia (much like our other little issue, but this time in 'reverse'). Recovery of this new disk rotation.... etc etc. I've lost count but this looks like a promising combination, at first glance. I seriously doubt it can go on ad infinitum without some additional input (potentially from all that output) but it seems like an interesting new FoR manipulation.

[Tusk]

I can orientate the magnet any where, not just next to the axle, and have the same reaction to either acceleration or deceleration of the rotor.

I had a quick look for an example of this Tom, a veritable junkyard of spinning tops and swinging doors; no luck so far though  Anyway you almost certainly realise that what you are seeing is a simple case of lever arm bias. The rotor goes one way, the stator, case, mounts etc go the other way (let's refer to these as simply 'the case'). Since the 'case' is attempting to rotate regardless of being mounted on a rotor arm, that part furthest from the rotor arm axis will have a greater lever arm advantage than the nearside, resulting in rotation of the rotor arm.

With the PE apparatus (as telecom kindly pointed out recently) the secondary reaction at the disk axis has no force pair, except inertia; unless we provide some other opposition such as that incurred when turning a generator. If we choose not to, and allow the secondary motion to spend itself uselessly, it might easily be interpreted as a lever arm bias with the various forces and motions in balance and accounted for. Two distinct and separate yet equal reactions in the same direction and originating from a single applied force must create an imbalance, or bias (as I prefer it). 

So while it seems unlikely we would see OU with a simple lever arm bias, the secondary force which manifests at the disk axis as described owes nothing in terms of the force which created it, that debt having been paid in full with the reaction at and rotation of the disk.

It's a 'freebie' 

[telecom]

Since this "free" force at axis of the disc doesn't have a reaction pair,
it may be an ideal candidate for a propulsion force!

[Tusk]

it may be an ideal candidate for a propulsion force!

I have to smile at that telecom, since this is full circle on how the investigation began. I was thinking about possible inertial drive systems myself   

Here's a rough sketch of my original idea, which immediately brought forth the paradox (bearing in mind that no paradox can survive it's own solution).

A quick description then; this is a twin disk system in equilibrium, the disks motivated equally by twin EM drive units as shown. The applied forces (on the disks innermost edges) are indicated in red, with the reactions to same indicated in black at the drive units. Also I have indicated the rotation of the disks.

The question then becomes: does the device accelerate, if so which way and if not then why?