Re: What is the difference between angular frequency and angular velocity?

It is unfortunate that the same symbol [w] can 
have slightly different uses, isn't it?  Usually the context of the use of the 
symbol tells you exactly how it's being used.

In the case of angular velocity and angular frequency they are almost the 
same, and, in fact, there is a subtle connection between the two that is the 
reason why the same symbol is used.  In simple harmonic motion the angular 
frequency can be considered the angular velocity of a simple circular motion 
whose projection is the simple harmonic motion!!  For instance, the s.h.m. 
(simple harmonic motion) of a mass on a spring can be considered the projection 
on a line of the motion of an equivalent mass that is going around in a circle 
whose diameter is the same as the difference in the limits of motion of the 
s.h.m. mass.

There are a number of previously-answered questions on our site which go into 
more (and probably better) detail than I have done.  Go to our search engine and 
search on "simple harmonic motion" or "harmonic motion".

John Link, MadSci Physicist


[Here is some HTML that should display the Greek characters for lower and upper 
case omega in many browsers:

wW


Take a look at the source code to see how it is done.]