Angular frequency

In physics (specifically mechanics and electrical engineering), angular frequency ω (also called angular speed) is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity. The term angular frequency vector ec{omega} is sometimes used as a synonym for the vector quantity angular velocity .

Related Topics:
Physics - Mechanics - Electrical engineering - Angular velocity

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

Related Topics:
SI - Radians - Second

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One revolution is equal to 2π radians, hence

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:omega = {{2 pi} over T} = {2 pi f} = v / r

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where

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

Related Topics:
Radian - Second

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:T is the period (measured in seconds),

Related Topics:
Period - Second

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:f is the frequency (measured in hertz),

Related Topics:
Frequency - Hertz

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

Related Topics:
Velocity - Metres per second

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

Related Topics:
Radius - Metre

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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 pi. In fact, it is used in many fields of physics involving periodic phenomena, such as quantum mechanics and electrodynamics.

Related Topics:
Quantum mechanics - Electrodynamics

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For example:

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a = - omega^2 x;

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

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:

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a = - 4 pi^2 f^2 x;

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