Example of a homogeneous, but not isotropic system

[greypilgrim]

Hi,

I have some trouble understanding if linear momentum and angular momentum (and their conservation laws) are completely independent or not. For example, one can calculate the angular momentum of a uniformly moving body with respect to a fixed point in space and show that it is indeed conserved. It doesn't work the other way around, the linear momentum of a uniformly revolving body is not conserved. This makes some sense from a Noetherian point of view, since the center of the circular motion must exert an isotropic force, which makes the system isotropic but not homogeneous.

Are there systems where linear momentum is conserved, but angular momentum is not? This would need a homogeneous, but not isotropic system, and I can't think of one (but I also have some trouble with the terms homogeneous and isotropic, so maybe there are very simple examples).

Thanks

 

[ShayanJ]

This thread will help you.

 

[greypilgrim]

Thanks, I will study this thread, but a very basic question first: If a system is isotropic, does this mean that there is (at least) one point in the system from which "the system looks the same if you look in any direction", or does this have to be fulfilled at any point in the system?