Spinning Spool Physics Q: Is Circumference Dist. = Center Dist.?

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Discussion Overview

The discussion revolves around the physics of a spinning spool and whether the distance traveled by the circumference is the same as the distance traveled by the center of the circle during rotation. The context includes a reference to a physics olympiad question and involves conceptual reasoning about motion and distance in rotational dynamics.

Discussion Character

  • Exploratory
  • Conceptual clarification

Main Points Raised

  • One participant questions if the distance traveled by the circumference of a spinning spool is equal to the distance traveled by its center when it makes a complete turn.
  • Another participant interprets the question as asking if the distance traveled equals the circumference when the spool rolls one complete turn.
  • A different participant notes that the top of the spool moves twice as fast as the center, raising a question about the implications of this observation when the spool is pulled under the center.
  • One participant suggests considering a very small movement to understand the rotation of the spool about its point of contact with the ground.

Areas of Agreement / Disagreement

Participants express different interpretations and reasoning regarding the motion of the spool, indicating that multiple competing views remain without a consensus on the question posed.

Contextual Notes

The discussion does not resolve the assumptions regarding the nature of the spool's movement or the definitions of distance in this context.

zabachi
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I have a question about a spinning spool, there is a spool spinning and is the sistance traveled by the circumference the same as the center of the circle? You can refer to the diagram attached for a question I had trouble with from a physics olympiad. The answer
was (B).
Thanks in advance!
 

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zabachi said:
I have a question about a spinning spool, there is a spool spinning and is the sistance traveled by the circumference the same as the center of the circle?
I assume you are asking: When the rolling spool makes one complete turn, has it traveled a distance equal to the circumference?

What do you think? (Cut out a circle and try it!)
 
zabachi said:
You can refer to the diagram attached for a question I had trouble with from a physics olympiad. The answer was (B).
The top of the spool moves twice as fast as the center. But what happens when you pull it under the center?

https://www.youtube.com/watch?v=dvyii6QBLtw
 
I think the easiest way to figure it out is to consider a very small movement. The spool as a whole rotates about its point of contact with the ground.
 

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