How reaction actually wheel works?

[Jovus]

How so, if it's a force exerted by the particles themselves?

[andrewas]

Momentum is a vector quantity. If friction between the two particles is bringing them to a complete rest, then they started with exactly opposite momentum vectors. Total momentum of the system was always zero.

[Shpaget]

I got confused when you said "Now we clearly agree that certain non-conservative forces (e.g. friction, B) can take energy out of the system, viz. reduce T. ".
To take the energy out of the system you need to act upon the system from outside of it. Friction inside the system does not take the energy out of it.

In your case of P = m1v1 + m2v2
v1 = -v2
P = m1v1 - m2v2, and if m1 = m2
P = 0
It was 0 from the beginning.

Ninjaed Edited November 23, 2015 by Shpaget

[CatmanFS]

I thought that the reaction wheels are just shifting weight around the spacecraft and changing it's center of mass. By shifting enough weight around you could do all sorts of stuff.