Confused about the speed of a point on a rotating body

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Discussion Overview

The discussion revolves around determining the velocity of a collar on a rotating system involving a disk and a slender rod. Participants explore the concepts of angular velocity, centers of rotation, and the dynamics of the system as it transitions from rest.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant notes that the velocity of any point on a rotating body is the angular speed times the radius, questioning where the radius is measured from in this context.
  • Another participant suggests that the center of rotation could be point C or G, indicating uncertainty about the correct reference point.
  • A participant highlights that the rod is both rotating and translating, comparing it to problems involving a ladder sliding against a wall.
  • There is a suggestion to draw a free-body diagram to help identify the center of rotation and clarify the forces involved.
  • One participant challenges the interpretation of the collar's motion, asserting that it is not rotating.

Areas of Agreement / Disagreement

Participants express differing views on the center of rotation and the motion of the collar, indicating that multiple competing interpretations exist without a clear consensus.

Contextual Notes

There are unresolved aspects regarding the definitions of the center of rotation and the dynamics of the system, particularly in relation to the collar's motion and the free-body diagram referenced.

kineticjustin
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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



kineticjustin said:
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?
 
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The radius is measured from the center of rotation.

But I suspect you have misunderstood the question - point C (the collar) is not rotating.
 
Would the center of rotation be C or G?
 
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.)
 

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