Infinite acceleration + KE gain

[MrVibrating]

Hi all. I knocked up some WM2D sims to try cancelling counter-torque from a motor, using 'inertial torque' from changing moment-of-inertia.

So for example, if we drag some orbiting mass inwards, we get a positive inertial torque, caused by conservation of angular momentum increasing speed to compensate the drop in MoI, so preserving their product.

Suppose we have two identical rotors, in free space (no gravity), connected by a motor.  We begin with them in uniform rotation - same speed and sign.

Then we fire the motor, decelerating one rotor to halt, whilst doubling the speed of the other.

Now, let's add an inertial torque to the decelerated rotor - upon activating the motor, we also begin dragging the decelerated rotor's mass inwards against CF force.  Control the radial speed, such that the inertial torque perfectly matches the motor's counter-torque.

What happens?  We get "over-unity" work efficiency from the motor.  The rise in rotational KE is greater than the torque * angle of the motor:

..however, the 'gain' is also precisely equal to the work done against CF force!  So, no gain at all, ultimately.

The interaction thus solves perfectly to unity.

So, what if we changed the means by which MoI is varied - what if there were some way of changing MoI without having to physically move mass in and out against axial centrifugal force?

It turns out there's an extremely simple means to do this - perform the radial translations (moving mass in and out) upon orbiting rotors instead!  Unlike axial inbound vs outbound CF integrals, orbital ones sum to zero!  Mutually cancelling!

Furthermore, we don't even need to physically perform the radial translation at all; the MoI suddenly converges to the net orbital mass focused at the locii of the orbiting axes the instant they begin to counter-rotate, hence we can cause a binary 'flip' in MoI states, merely by switching an orbiting motor on and off!

So we can cause the same change in MoI, both by applying torque to the orbiting axes, as by physically moving the masses into their axial centers!  Here it is in action:

As you can see, the 'inertial torque' caused by this sudden MoI change is equal in sign and magnitude to the conventional torque - and counter-torque - being applied by the motors.. the latter two cancel out, leaving just the inertial torque.

The orbiting rotors are decelerated by 1 rad/s, the central one accelerates by 1 rad/s, net input torque * angle is zero, net momentum never once wavers, and because conservation of momentum applies at lightspeed... we get an instantaneous change in velocity!  

The acceleration is either "infinite", or else, there's no acceleration phase at all to speak of (a philosophical matter perhaps)..  

So the binary change in MoI accompanies a binary change in velocity and rotational KE!

I've put a small archive of examples together, including more detailed explanations of the exploit, here:

https://drive.google.com/open?id=1P1tlUn7THSKZ0CjWaFHFzFtOfrYVY6Ls

I think i may be somewhat out of my depth at this point..

 

- Please don't insta-ban me, mods! This is a genuine measurement with dual independent derivations of output energy, and standard F*d integrals for input energy - the latter have also been solved in terms of power * time with zero deviation, i just left those out to minimise complexity..  further examples / control cases etc. available on request.  No innovations, it's just momentum and KE, using only the standard formulas throughout..

 

Edited February 6, 2019 by MrVibrating
image tags not working!

[wtf]

I don't know what it is but it's pretty cool!

[studiot]

7 hours ago, MrVibrating said:

Suppose we have two identical rotors, in free space (no gravity), connected by a motor.  We begin with them in uniform rotation - same speed and sign.

Then we fire the motor, decelerating one rotor to halt, whilst doubling the speed of the other.

 

How does that work if the rotors are going in the same direction ?