# Example of a homogeneous, but not isotropic system

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1. Oct 25, 2014

### 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

2. Oct 25, 2014