Sum of torque

[EOW]

If the ring is turning at w2 and the arm is turning at w1 with w2 < w1, I take 2 external blue objects that are turning at w1, like the ring turns counterclockwise in the arm reference, it's possible to eject these 2 objects and apply a clockwise torque to the ring in the same time. The two external objects don't lost the energy from the rotation w1 and win energy from the ring. Like this:

[EOW]

The arm is turning clockwise at w1 and the ring is turning at w2, with w2 < w1. With one external object, free to move in space, that move in a straight line at the velocity V.

There is a shock at time = 1, IN HORIZONTAL AXIS (the shock is not in vertical axis), between the blue object and the ring.

The trajectory of the ring is more at left than at right (look at image)

For example, with:

r=1
d=3
w2=0
w1=10
t=1e-5

the result is :

9.9999e-5 at left
9.9985e-5 at right

So the shock move at left the free object and increases the kinetic energy of the ring. The arm don't receive a torque because the force is in the axis.

I did a video:

https://www.youtube.com/watch?v=HWZBj_WiPHA

[EOW]

The black arm is turning clockwise at w1. The red ring is turning clockwise at w2 with w2 < w1. There are 2 magenta disks that are turning at w3 around themselves. The grey arm is turning at w1 at start. The grey arm can turn around itself. Magenta disks are perpendicular at the ring. There is friction between the red ring and magenta disks, this gives a force F (I guess F constant even rotationnal velocity is changing with time).

[EOW]

Edit: Consider the grey arm like a gyroscope, like that the torque on the grey arm don't move the grey arm around the blue axis but around a perpendiculary axis. And like this the grey arm don't lost energy. There is only friction, w2 is increasing and w3 is increasing too.

[EOW]

With only the black arm, the red ring and the gyroscope. The gyroscope must turn at w1 at start.