azimuthal

Azimuthal is an adjective used to describe anything relating to the azimuth, the angular coordinate that specifies direction around a fixed axis. The term appears in several disciplines, notably geometry, navigation, astronomy, and physics, where it helps distinguish lateral orientation from other angular components.

In spherical and cylindrical coordinate systems, the azimuthal angle describes position around the axis. In many conventions, it is the angle in the horizontal plane measured from a reference direction, with the exact symbol and zero point varying by context. The complementary polar or inclination angle then describes the tilt away from the axis. The concept is central to describing directions, trajectories, and locations on a sphere or in space.

Azimuthal symmetry refers to invariance under rotations about a particular axis. Such symmetry implies conservation of the corresponding angular momentum component in physics and often simplifies mathematical treatments of systems ranging from cylindrical objects to planetary orbits and quantum-mechanical problems.

In quantum mechanics, the azimuthal quantum number, commonly denoted l, is the angular momentum quantum number. It takes nonnegative integer values (0 to n−1) and determines the shape of atomic orbitals as well as the magnitude of orbital angular momentum. The term “azimuthal” here highlights the association with rotation around an axis and the corresponding angular properties.

Other uses include azimuthal map projections in cartography, which preserve directions from a central point, and azimuthal distributions in particle and Earth sciences, where angular data around an axis is analyzed.