Angular frequency (ω) is a scalar quantity that shows how fast the phase of a sine wave or oscillation changes with time. It measures the rate of change in angular displacement and is expressed in radians per second. It describes how quickly an object completes one full rotation or oscillation in circular motion.
It is related to frequency, which tells the number of cycles per second, and 1 hertz is approximately equal to 6.28 rad/s. Angular frequency is widely used in physics, engineering, and mathematics to describe periodic motion and wave behavior.
\omega = \frac{2\pi}{T}
where,
- ω (omega) = angular frequency,
- π (pi) = 3.14159.
- T = time period of rotation (time taken for one complete cycle of rotation)
Angular frequency is measured in radians per second (rad/s) and represents the rotational speed of an object. It is widely used in mechanics, electromagnetism, and wave theory.
SI Unit: rad/s
Dimension: T-1 (inverse of time)