Angular Velocity versus Angular Frequency

[Jimmy87]

Hi pf, I have been looking at previous threads and internet sites and I am still a bit confused when you use the term angular frequency as oppose to angular velocity and vica versa. For example, if you are looking at the oscillation of a spring then the equation for the instantaneous displacement is given by:

x = a sin(ωt)

In this case does ω refer to the angular frequency or velocity and why? Please could someone provide me with two situations, one where you clearly refer to it as angular velocity and the other referring to angular frequency?

Many thanks in advance!

 

[jtbell]

In the context of oscillatory motion (such as your example) I would call ω the "angular frequency".

In the context of rotational or circular motion, I would call it the "angular velocity." For example, an old fashioned phonograph record rotates with an angular velocity of 33 1/3 rpm = about 3.5 rad/s.

 

[AlephZero]

I think "angular velocity" should only be used to describe a real physical rotation, and strictly speaking it is a vector quantity. The direction of the vector is the along the axis of rotation.

The fact that it angular velocity is a vector might not seem very important in a first course in dynamics, when the axis of rotation is usually fixed in space and "obvious", but in more advanced problems the rotation axis is not necessarily fixed - for example, think about the motion of a spinning top as it slows down, or the motion of a spacecraft .

"Angular frequency" is used instead of "the magnitude of the angular velocity vector", and also for "frequency in radians per second" when describing simple harmonic motion etc, as in the OP's equation x = a sin(ωt).