Angular frequency

Angular frequency is the rate at which a periodic phase changes over time, measured in radians per unit time. It relates a cycle’s frequency to its angular phase.

Phase: A position within a repeating cycle, commonly represented as an angle. Angular frequency measures how quickly this quantity advances.
Radian: The angle subtended at a circle’s center by an arc equal in length to its radius. Radians make phase change per time directly expressible as angular frequency.
Wave number: The spatial rate of phase change in a wave, measured in radians per unit distance. Together, angular frequency and wave number specify phase change in space and time.
Ordinary frequency: The number of cycles of a periodic process per unit time, measured in hertz. It counts cycles, whereas angular frequency counts radians of phase per unit time.
Frequency: The number of repeating cycles completed per unit time. Multiplying frequency by one full turn in radians gives angular frequency.
Circle: A plane curve whose points are all equally distant from a fixed center. One full revolution supplies the 2π-radian phase change per cycle.
Dispersion relation: A relation connecting a wave’s angular frequency to its wave number. It determines how angular frequency varies across wave modes.
Angular velocity: The rate of change of an object’s angular position over time. It describes rotation of a physical object; angular frequency tracks phase progression.
Period (physics): The time required for one complete cycle of a periodic process. Angular frequency equals one full turn divided by the period.
Periodic function: A function that repeats its values at regular intervals of its input. Angular frequency describes the time rate of phase progression in periodic functions.

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