Why does a rotating chain become horizontal?

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SUMMARY

The discussion centers on the behavior of a rotating chain, specifically why it tends to assume a horizontal position when spun rapidly. Key equations referenced include angular momentum (L=I ω) and kinetic energy (E=1/2 I ω²). The confusion arises from the relationship between moment of inertia and energy, with participants clarifying that the chain's highest moment of inertia correlates with its horizontal orientation during rapid rotation. The use of free body diagrams (FBD) is suggested as a method to model the chain's behavior accurately.

PREREQUISITES
  • Understanding of angular momentum and kinetic energy equations
  • Familiarity with moment of inertia concepts
  • Basic knowledge of free body diagrams (FBD)
  • Experience with rotational dynamics
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  • Study the principles of rotational dynamics in detail
  • Learn how to construct and analyze free body diagrams (FBD) for distributed systems
  • Explore the relationship between moment of inertia and angular velocity
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Students of physics, educators teaching rotational dynamics, and anyone interested in the mechanics of rotating systems will benefit from this discussion.

Lindsayyyy
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Hi

Homework Statement



A chain rotates fast. Observation: the chain gets into a horizontal position. Why?



Homework Equations



L=I \omega E= \frac 1 2 I \omega² E=\frac 1 2 \frac {L²} I



The Attempt at a Solution



Well, I have two equations for the energy. I know that I have to use the second one, because when I do the experiment I see that the chain "uses" its highest moment of intertia. But I can't I use the first equation for the energy which implies that the chain has to use the smallest moment of inertia to have the minimum energy?

Where is my mistake?

Thanks for help.
 
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Lindsayyyy said:
Hi

Homework Statement



A chain rotates fast. Observation: the chain gets into a horizontal position. Why?



Homework Equations



L=I \omega E= \frac 1 2 I \omega² E=\frac 1 2 \frac {L²} I



The Attempt at a Solution



Well, I have two equations for the energy. I know that I have to use the second one, because when I do the experiment I see that the chain "uses" its highest moment of intertia. But I can't I use the first equation for the energy which implies that the chain has to use the smallest moment of inertia to have the minimum energy?

Where is my mistake?

Thanks for help.

Is the problem asking about swinging a chain around in a circular motion overhead? If so, it never makes it to horizontal, right? It can get close if swung very fast, but it can never be horizontal if there is a vertical gravitational field.

Can you just approach this problem using a free body diagram (FBD)? To model the chain (as opposed to a weight on a string), you would need to do a distributed FBD with something like 10 weights evenly distributed along the chain length, joined by short strings. With that kind of FBD, you can show how the "chain" tends to become more horizontal as it is swung faster and faster in a circle...
 
I think I found my mistake. Is it true that the angular velocity is the lowest when the chain rotates around its biggest moment of inertia? If so, I get it ^^
 

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