Why does a rotating chain become horizontal?

AI Thread Summary
A rotating chain tends to become horizontal due to the dynamics of angular momentum and energy conservation. The discussion revolves around the confusion between using different equations for energy, specifically how the chain utilizes its moment of inertia during rotation. It is clarified that while the chain can approach a horizontal position when swung rapidly, it cannot achieve a completely horizontal orientation in a vertical gravitational field. The use of a free body diagram (FBD) is suggested to better understand the forces acting on the chain and its behavior during rotation. Ultimately, the relationship between angular velocity and moment of inertia is key to resolving the confusion in the problem.
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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