What is the difference between angular velocity and angular frequency?

Question

And when are they considered the same?

Answer 1

The relationship between angular frequency and angular velocity comes from a relationship between uniform circular motion and simple harmonic motion.

 

If an object goes around a circle once in a certain time t (in seconds), it has traveled through 2π radians in angle, and its angular velocity is thus 2π/t radians per second.

 

But traveling around a circle is akin to simple harmonic motion, because you go through a cycle and end up in the same place.  We can make an analogy between a cycle in simple harmonic motion and going around a circle once in uniform circular motion.  Thus, going through one cycle of simple harmonic motion in a certain time t (in seconds) can be described as going through 2π radians in that time, and -- since the number of cycles gone through per second is frequency, this is "frequency described by radians;"  thus, angular frequency.  It describes simple harmonic motion just as well as it describes motion around a circle at constant speed.

Answer 2

Edona,

         In the standard physics terminology ω (omega) usually stands for "angular velocity" and is measured in radians/second. f stands for "angular frequency" measured in hz or cycles per second.

The relationship between the two variables is:

 

ω=2πf

 

Hope this helps

 

Jim