Sum of torque

[EOW]

I made a mistake R1 must be < R2, so value can be:

Vleft=-R1w2+(R1−d)w1
Vright=-R2w2+(R2−d)w1 With:
R1=0.5
R2=15
w1=10
w2=8
d=4
I find:
Vleft=-49
Vright=-20

Add a translation for have +30:

Vleft= -19
Vright=+10

CQFD

[EOW]

I think like that it's correct, someone can verify ?

[EOW]

If I take a simple example. Trajectories are in doted lines. F1/F2 are created with a shock from external object. F11/F21 create a torque on ring, this increase the energy of disk. F12/F22 create a force to blue axis, this axis is free to move in space, so forces can't give a torque on axis but only move it, this give energy too. For simplify the problem, think with mass of blue axis like very high compared to the grey ring. I think like that the energy is not constant.

[EOW]

I forgot a 2 forces, so there is a torque on black arm, this decrease energy. But the force (F12+F22) on blue axis move all the system, this must increase a little its energy, no ? What's the difference between fixed blue axis and free ? Fixed blue axis F12+F22 don't works and free F12+F22 works.

[EOW]

It's seems it's not possible to have trajectories like I want. But it's possible to add N system in parallel. Each system give two energy E1 in heating and energy from disk E2. Sum for each disk is 2E1+E2. With N system this will give N(2E1+E2). I need to add energy at 2 last systems, need 2E1, so the sum of energy is N(2E1+E2)-2E1.

edit: for have friction, it's possible to place blue axis of rotation further (or closer), and change the angle, like angles can be shows between black and magenta lines. Add 3° at each new system. It's only for have "constact" during a time for have friction.

edit: in a last message I said it's not possible to find 2 points where horizontal velocity is negative, but it's possible with r > d (the mass is in the green point only, not at all the surface of the disk). Like that I can think like that: hits only one ball, and for have a torque I give the energy for this, like that I recover energy from ball but I lost energy I gave, BUT th energy of the disk increase !