Angular frequency
From Free net encyclopedia
Image:Angularvelocity.png 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 <math>\vec{\omega}</math> 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 T −1 since radians are dimensionless.
One revolution is equal to 2π radians, hence
<math>\omega = {{2 \pi} \over T} = {2 \pi f} = v / r</math>
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), and 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 <math>\pi</math>. In fact, it is used in many fields of physics involving periodic phenomena, such as quantum mechanics and electrodynamics.
For example:
- <math>
a = - \omega^2 x\; </math>
Using 'ordinary' revolutions-per-second frequency, this equation would be:
- <math>
a = - 4 \pi^2 f^2 x\;
</math>
Another often encountered expression when dealing with small oscillations is:
- <math>
\omega^{2} = \frac{k}{m} </math>
where <math>k</math> is the spring constant and <math>m</math> is the mass of the object.
See also
da:Vinkelfrekvens de:Kreisfrequenz es:Velocidad angular fr:Vitesse angulaire it:Velocità angolare ms:Frekuensi angular nl:Hoeksnelheid pl:Pulsacja sl:kotna hitrost fi:Kulmataajuus vi:Tần số góc