Understanding Dumbbell Rotation: Laws and Material Constants

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Discussion Overview

The discussion revolves around the dynamics of a dumbbell's rotation, particularly how the motion of one end affects the other when torque is applied. Participants explore the implications of material properties, specifically focusing on the behavior of a rubber or copper middle bar and how it influences the rotational motion over time.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions the relationship between torque applied to one end of a dumbbell and the resulting motion of the other end, particularly considering the material properties of the connecting bar.
  • Another participant suggests that the middle bar could exhibit a torsion-spring effect due to its material properties, indicating that no materials are perfectly rigid.
  • A later reply references the concept of torsion in mechanics and provides a formula for the spring constant of a beam under torsion, suggesting it may be relevant to the discussion.

Areas of Agreement / Disagreement

Participants express varying views on how material properties affect the rotational dynamics of the dumbbell, indicating that multiple competing perspectives remain on the topic.

Contextual Notes

There are unresolved questions regarding the specific material constants that should be considered and how to accurately model the behavior of the middle bar under torque.

Antti
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I just thought about a dumbbell (for some reason) and how one end rotates if I turn the other. If it was just a "mathematical system" with two flat cylinders and a long cylinder in between, then one end would rotate in exactly the same way as the other. But if the middle bar was rubber for example, then the rotation would be delayed in the other end. Now, is there some law describing the motion [tex]\theta(t)[/tex] of the other end if I know [tex]\tau(t)[/tex] (torque as function of time) of the first end. That is, if I also know the length of the middle bar and what it is made of? What material constants come into play? Could I model the bar with a simple spring instead?
 
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tiny-tim said:
Hi Antti! :smile:

(nobody else has replied, so: )

Does this help … http://en.wikipedia.org/wiki/Torsion_spring? :smile:

Well no. Say I had a dumbbell made entirely of Copper and I knew the exact shape of the whole thing. Then I'm thinking there should be some torsion-spring effect, though small, in the middle bar when I apply a torque to one end. No materials are perfectly rigid. How do you calculate this from the dimensions of the object and some (which?) material constants?
 
Try http://en.wikipedia.org/wiki/Torsion_(mechanics)" , which gives the spring constant ([itex]L/JG[/itex]) of a beam under torsion.
 
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