# Angular frequency and angular velocity in UCM and SHM

1. ### al_famky

29
this is another conceptual question, so sorry for not following the template.
I thought that angular frequency and angular velocity shouldn't be the same thing, but after going through some of the forum threads, there was the idea: "the only difference between angular frequency and angular velocity is ---the former is a scalar and the latter is a vector. They have the same magnitudes. "
which got me quite confused, because in general simple harmonic motion, angular frequency is constant and angular velocity is a varible...as in a pendulum or other motions.
so i was wondering if someone could enlighten me on the matter? Thank you.

2. ### BruceW

3,598
These words can have different meanings, which is why it can be confusing at times. You are correct that the speed of a pendulum in the angular direction changes with time. And now, angular frequency, well it depends how you define it. If you define it as 2PI/T then yes, you are correct that for SHM, the angular frequency will be a constant. But if you define it as the speed in the angular direction, divided by the length of the pendulum, you can see that it is a variable.

So I think that you have the concepts correct. It is where people are using different definitions for the same word which has confused you. This does happen quite a bit in physics unfortunately. So you just need to be careful which definition is being used. And when you get really comfortable with a subject, you can often guess which definition a person is using, even though they don't explicitly state it.

3. ### mukundpa

507
In an ideal SHM nothing rotates or circulates. The motion of the particle is in straight line, to and fro about the equilibrium position. As the motion is periodic and the displacement, velocity and acceleration are sinusoidal functions of time, we can represent this motion as the projection of circular motion of a (imaginary) particle on a straight line. Thus every simple harmonic motion can be referred as projection of circular motion of an imaginary particle called reference particle. Angular velocity of this reference particle is called angular frequency. It has noting to do with the angular velocity of the pendulum bob.
If we consider oscillations of a spring mass system these are simple harmonic. It will have angular frequency equal to sq.rt (k/m) but there is nothing like angular velocity.

4. ### al_famky

29
Thank you very much, BruceW and mukundpa, it was really enlightening reading your explanations!