Angular frequency
From Wikinfo
In physics (specifically mechanics), angular frequency ω (sometimes called angular velocity) is a measure of rotation rate, almost invariably given in units of radians per second, or simply s−1 since radians are dimensionless. One revolution is equal to 2π radians, hence
- <math>
\omega = {{2 \cdot \pi} \over {T}} = {2 \cdot \pi \cdot f} </math>
where T is the period and f is the frequency.
Using angular frequency instead of ordinary frequency is convenient in many applications, as it avoids the excessive appearance of π. 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' frequency, this equation would be:
- <math>
a = - 4 \pi^2 f^2 x\;
</math>
Note also that
- <math>
T=2\pi v/r \;
</math>
and therefore that
- <math>
\omega=2\pi/T=v/r.\; </math>
Where T is the period and v is the velocity.
See also
- Radian[[it:Velocit� angolare]]
References
- Adapted from the Wikipedia article, "Angular_frequency" http://en.wikipedia.org/wiki/Angular_frequency, used under the GNU Free Documentation License
