Angular frequency

Do not confuse with angular velocity

Angular frequency is a measure of how fast an object is rotating

In physics (specifically mechanics and electrical engineering), angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, and radian frequency) is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity. The term angular frequency vector Failed to parse (Missing texvc executable; please see math/README to configure.): \vec{\omega}

is sometimes used as a synonym for the vector quantity angular velocity .

In SI units, angular frequency is measured in radians per second, with dimensions s⁻¹ since radians are dimensionless.

One revolution is equal to 2π radians, hence

Failed to parse (Missing texvc executable; please see math/README to configure.): \omega = {{2 \pi} \over T} = {2 \pi f} = \frac {v} {r}

where

ω is the angular frequency or angular speed (measured in radians per second),

T is the period (measured in seconds),

f is the frequency (measured in hertz),

v is the tangential velocity of a point about the axis of rotation (measured in metres per second),

r is the radius of rotation (measured in metres).

Angular frequency is therefore a simple multiple of ordinary frequency. However, using angular frequency is often preferable in many applications, as it avoids the excessive appearance of Failed to parse (Missing texvc executable; please see math/README to configure.): \pi . In fact, it is used in many fields of physics involving periodic phenomena, such as quantum mechanics and electrodynamics.

For example:

Failed to parse (Missing texvc executable; please see math/README to configure.): a = - \omega^2 x \;

Using 'ordinary' revolutions-per-second frequency, this equation would be:

Failed to parse (Missing texvc executable; please see math/README to configure.): a = - 4 \pi^2 f^2 x\;

Another often encountered expression when dealing with small oscillations is:

Failed to parse (Missing texvc executable; please see math/README to configure.): \omega^{2} = \frac{k}{m}

where

Failed to parse (Missing texvc executable; please see math/README to configure.): k

is the spring constant

Failed to parse (Missing texvc executable; please see math/README to configure.): m

is the mass of the object.

Angular frequency inside an LC circuit can also be defined as the inverse of the square root of the capacitance (measured in farads), times the inductance of the circuit (in henrys).

Failed to parse (Missing texvc executable; please see math/README to configure.): \omega = \sqrt{1 \over LC}

See also

• Frequency
• Radian
• Simple harmonic motioncs:Úhlová frekvence

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