What Does Azimuthal Symmetry Mean in Physics?

[ahmad1992]

Anyone can explain me what is the physical meaning of azimuthal symmetry?
Based on the book, azimuthal symmetry means when m=0.
However how can we determine that a system is azimuthal symmetry or not?
Like for example, I have a two concentric spheres with radius a and b and hold at different potential.

 

[ShayanJ]

A system has azimuthal symmetry, if there exists an axis of rotation(usually called the z axis), such that if you rotate the system by an angle $0 \leq \phi \leq 2\pi$ around that axis, it doesn't change.

 

[Meir Achuz]

Like for example, I have a two concentric spheres with radius a and b and hold at different potential.

That system has spherical symmetry, which includes axial symmetry.