Conservation of Energy applied to A system with Rotation and Translati

[kineticjustin]

Problem Statement:

The system consists of a 20-lb disk A, 4lb slender rod BC, and a 1-lb smooth collar C. If the disk rolls without slipping, determine the velocity of the collar at the instant theta=30 degrees. The system is released from rest when theta= 45 degrees.

Above I attached a photo of what my FBD for the question looks like. When solving the question, the velocity of point B was described as 1.5*w(bc). I understand that the velocity of of any point of a rotating body is the angular speed times the radius, so where is the radius measured from? The rod is rotating about Point B isn't it?

 

[kineticjustin]

I should mention that the length of rod BC is 3ft.

 

[etudiant]

An interesting setup.
The rod may be pivoting about point B, but is also exerting an impulse on B, which brings the disk into rolling.
The disk rolls under the impulse of the falling 1 pound weight C and the falling 4 pound rod BC.
Not all of the potential energy in the weight and rod are transformed into kinetic energy of the disk, only the horizontal component. The radius of the disk is the measured element.