Angular Velocity and Angular Frequency

[zhaos]

Homework Statement

Hi all, I am a bit confused about angular frequency, specifically in the case of a pendulum (bob pendulum or physical pendulum). Also, what's the difference between angular frequency and angular velocity?

Homework Equations

I understand that a physical pendulum is governed by the relation theta = theta_max Cos (omega*t + phi), where omega = (kappa/I)^1/2, where -kappa*theta = torque. But also if I take a derivative with respect to time, I get d theta/dt = - omega*theta_max*Sin(omega t + phi). Isn't this d theta/dt also omega? But, say, when d theta/dt is maximal, d theta / dt = omega' = omega * theta_max

The Attempt at a Solution

My question is, what is the difference between these two omegas? Is it even appropriate for me to call d theta / dt, omega? Additionally, the tangental speed a distance r from the center of mass is v = r*omega. But should I be using omega or d theta/dt? My textbook doesn't explain this to me. Thanks for giving this a look over.

 

[zhaos]

a small bump?
This was a conceptual question I had, not relating to any actual HW problem, so perhaps I shouldn't have asked it in this section.
But basically it's either omega = (kappa/ I)^(1/2) or it's omega' = omega*thetamax*cos(omega*t), where omega in the second equation is defined by the first equation. Whereas the first, angular frequency?, is a constant, the second one varies with time and is the first one multiplied by theta max. So again, I am unsure what these values mean. I understand angular frequency to mean the angular speed of an oscillatory motion if you take the circle it is tracing out. i.e., if you had an object moving at a constant angular speed in a circle, if you looked at the object from the side of the circle, you would see the object in oscillatory motion.

Thanks