Confused about the speed of a point on a rotating body

[kineticjustin]

Homework 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.

Homework Equations

v=wr

The Attempt at a Solution

View attachment 63865

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 when considering the speed of a point on a rotating body? The rod is rotating about Point B isn't it?

 

[Simon Bridge]

The radius is measured from the center of rotation.

But I suspect you have misunderstood the question - point C (the collar) is not rotating.

 

[kineticjustin]

Would the center of rotation be C or G?

 

[Simon Bridge]

The rod is certainly turning - but it's also translating (well, it's center of mass is).
It's rather like those problems with a ladder leaning against a wall and sliding isn't it?

How could you go about figuring the center of rotation - could it be B?
Why not draw a free-body diagram and place the forces on it and let them tell you?
(Your attachment, btw, is not a free body diagram.)

 

[rezeew]

The radius in this case is measured from the center of rotation, which is point B. The velocity of point B is given by v=wr, where w is the angular velocity and r is the radius from the center of rotation. In this case, the radius is equal to the length of the rod BC. So, the velocity of point B can be written as v=wr=1.5*w*BC. This is because point B is rotating about its own axis, which is also the axis of rotation for the entire system.

It is important to keep in mind that the velocity of a point on a rotating body is always perpendicular to the radius vector. So, in this case, the velocity of point B is perpendicular to the rod BC. I hope this helps clarify any confusion regarding the speed of a point on a rotating body.