Question

How is angular frequency different from angular velocity? I mean we can tell intuitively what angular velocity is but what’s the intuitive explanation of angular frequency?

Answer 1

Hint: This is a tricky question, as the symbol to represent angular velocity and angular frequency is the same, but the meaning of both the term is different. The formula for both the terms is different and the use of both the terms also differ from each other. Angular frequency is related to displacement and angular velocity is related to the velocity of revolution.

Complete answer:
Angular frequency $\omega $ (also referred to by the terms angular speed, radial frequency, circular frequency, and orbital frequency) is a scalar measure of rotation rate. It refers to the angular displacement per unit time (e.g., in rotation) or the rate of change of the phase of a sinusoidal waveform (e.g., in oscillations and waves), or as the rate of change of the argument of the sine function. Angular frequency (or angular speed) is the magnitude of the vector quantity angular velocity.
One revolution is equal to $2\pi $ radians, hence
$\omega =\dfrac{2\pi }{T}=2\pi f$
where,
$\omega $ is the angular frequency or angular speed (measured in radians per second),
$T$ is the period (measured in seconds),
$f$ is the ordinary frequency (measured in hertz).
Angular velocity is that velocity which acts on revolution or rotation of a body with a certain angle with axis with valid radius, i.e., the rate of change of angular rotation.
Angular velocity, $\omega =\dfrac{d\theta }{dt}$
There are two types of angular velocity: orbital angular velocity and spin angular velocity. Spin angular velocity refers to how fast a rigid body rotates with respect to its center of rotation. Orbital angular velocity refers to how fast a point object revolves about a fixed origin, i.e. the time rate of change of its angular position relative to the origin. Spin angular velocity is independent of the choice of origin, in contrast to orbital angular velocity which depends on the choice of origin. In general, angular velocity is measured in angle per unit time, e.g. radians per second.

Note:
In this type of question, first understand the definition of each term and then understand the application of it, so that it can help to differentiate between the two terms. The symbol for both the terms is the same but the formula is different, be careful before applying the formula or else it may give the wrong result.