Angular Frequency

Angular frequency, abbreviated as \(\omega\) (Greek symbol omega), also known as radial frequency or circular frequency, is a used in physics and engineering to describe the rate of change of the phase of a sinusoidal waveform.  It is closely related to frequency, which measures the number of cycles or oscillations of a waveform per unit of time.  Angular frequency is a more convenient way to work with sinusoidal functions in various mathematical and physical contexts.

Angular frequency is particularly important in fields like electrical engineering, where it is used to describe the behavior of alternating current (AC) circuits, as well as in mechanical systems and wave phenomena in physics.  It helps describe the phase and frequency characteristics of sinusoidal oscillations and waves.

 

Angular Frequency for Oscillating Object formula
\( \omega \;=\; 2 \; \pi \; f  \)     (Angular Frequency) \( f \;=\; \omega \;/\; 2 \; \pi \)
Symbol	English	Metric
\(\large{ \omega }\)  (Greek symbol omega) = Angular Frequency	\(deg \;/\; sec\)	\(rad \;/\; s\)
\(\large{ \pi }\) = Pi	\(3.141 592 653 ...\)	\(3.141 592 653 ...\)
\(\large{ f }\) = Frequency	\(Hz\)	\(Hz\)

  

Angular Frequency for Rotating Object formula
\( \omega \;=\; \Delta \theta \;/\; \Delta t \)     (Angular Frequency) \( \Delta \theta  \;=\; \omega \; \Delta t  \) \( \Delta t \;=\; \Delta \theta \;/\; \omega \)
Symbol	English	Metric
\( \omega \)  (Greek symbol omega) = Angular Frequency	\(deg \;/\; sec\)	\(rad \;/\; s\)
\( \Delta \theta \) = Rotation Change	\(deg\)	\(rad\)
\( \Delta t \) = Time Change	\(sec\)	\(s\)