Question About the signifficance of energy

[FNL]

In the course of theoretical physics by Landau et Lifshitz volume 05 §4 (the signifficance of energy ) we have:
"
The momentum and angular momentum of a closed system depend on its motion as a whole (uniform translation and uniform rotation). We can therefore say that the statistical state of a system executing a given motion depends only on its energy. In consequence, energy is of exceptional importance in statistical physics.
"
My question , or what I can't understand is how it comes that (momentum and angular momentum of a closed system depend on its motion as a whole); while energy does not depend on that motion in order to get that importance for the distrubtion function?

 

[Simon Bridge]

The second sentence does not follow from the first... you need another statement to add to it. What does "statistical state" mean here?

But per your question: the momentum of a system is the velocity of it's center of mass multiplied by it's mass right? ie. the system momentum depends on it's bulk motion. If no motion, then momentum zero.
You can also derive the bulk momentum from the momentum of it's constituents.

 

[FNL]

Thank you for the response.
It's just that seeming non-correlation between the two sentences what make me confused.

By the way what you have said about momentum does not apply to angular momentum, angular momentum comport like energy when one talks about the decomposition of motion into intrinsic and bulk ones.

I'll write the equations that related the galilean and the centre of mass systems (in the usual notation):

P= P'+MV =MV (P'=0 In CM frame)
L=L'+R×MV
E=E'+1/2MV² (for isolated system)As one can see it's only momentum whose depends entirely on the motion of the system as a bulk. angular momentum like energy have a non-zero intrinsic part.