# Angular Velocity

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Angular velocity, abbreviated as $$\omega$$ (Greek symbol omega), also called angular speed, is the speed that an object moves through an angle, θ.  The calculation below calculates ω but does not calculate the relative velocity of a point as it moves throughout the curve.

## Angular Velocity formula

 $$\large{ \omega = \frac { \Delta \theta } { \Delta t } }$$ $$\large{ \omega = \frac { \theta_f \;-\; \theta_i } { \Delta t } }$$ $$\large{ \omega = \frac { 2 \; \pi } { \Delta t } }$$

### Where:

 Units English Metric $$\large{ \omega }$$   (Greek symbol omega) = angular velocity $$\large{\frac{deg}{sec}}$$ $$\large{\frac{rad}{s}}$$ $$\large{ \Delta \theta }$$   (Greek symbol theta) = angular displacement $$\large{deg}$$ $$\large{rad}$$ $$\large{ s }$$ = displacement covered by object $$\large{ft}$$ $$\large{m}$$ $$\large{ \theta_f }$$ = final angle $$\large{deg}$$ $$\large{rad}$$ $$\large{ \theta_i }$$ = initial angle $$\large{deg}$$ $$\large{rad}$$ $$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$ $$\large{ r }$$ = radius $$\large{ft}$$ $$\large{m}$$ $$\large{ \Delta t }$$ = time change $$\large{sec}$$ $$\large{s}$$