Proofing Moment of Inertia Solid Sphere

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Homework Help Overview

The discussion revolves around deriving the moment of inertia for a solid sphere, specifically questioning the applicability of a "pyramid" method, which is likened to slicing a watermelon. The original poster expresses uncertainty regarding the approach and the necessary elements for the calculation.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the validity of using the pyramid method for deriving the moment of inertia, with some suggesting that slicing the sphere into discs may be more effective. Questions arise about the elements of volume and moment of inertia needed for the calculations.

Discussion Status

The discussion is ongoing, with participants providing insights into the proposed method and questioning its effectiveness. There is a recognition of confusion regarding the elements involved in the calculations, and some guidance is offered regarding alternative slicing methods.

Contextual Notes

Participants note that the original poster has not provided a detailed attempt at the problem, which is required by forum rules. There is also mention of differing opinions on the ease of the proposed method based on lecture content.

chocophysuny
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Homework Statement


Can i use "pyramid" method to derive the equation of Moment Inertia solid sphere?
The pyramid is such we slice a watermelon.
Sorry for my bad english.
Regards.


Homework Equations



2/5 MR^2

The Attempt at a Solution

 
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Hello chocophysuny,
Welcome to Physics Forums,

chocophysuny said:
Can i use "pyramid" method to derive the equation of Moment Inertia solid sphere?


Have you tried it? You must show what you have tried to get help on PF (forum rules).

Sunil
 
It doesn't seem to me that it would be a useful approach. It does not simplify anything. You need to slice it into elements that have an easily calculated MI, such as discs perpendicular to the axis of rotation.
 
haruspex said:
It doesn't seem to me that it would be a useful approach. It does not simplify anything. You need to slice it into elements that have an easily calculated MI, such as discs perpendicular to the axis of rotation.

But my lecture say this method is easy enough to solve.
And, actually i confused to find the element of volume and element of MI.

So, in your opinion, this is not solvable?
 
Sunil Simha said:
Hello chocophysuny,
Welcome to Physics Forums,




Have you tried it? You must show what you have tried to get help on PF (forum rules).

Sunil

Yes, I've tried it. But i didn't find the solution.
I'm confused with the element of volume and element of pyramid

"To find MI from the element, we need element of volume and element of MI, isn't it?"
 
chocophysuny said:
"To find MI from the element, we need element of volume and element of MI, isn't it?"

I'm sorry, I didn't understand what you meant there.
 
chocophysuny said:
But my lecture say this method is easy enough to solve.
And, actually i confused to find the element of volume and element of MI.

So, in your opinion, this is not solvable?

Maybe I misunderstand the proposed method. From your watermelon analogy, I assumed it involves slicing the sphere into thin wedges using planes through the axis of rotation. If so, I think you would then need to cut each wedge into laminae, either rectangular ones parallel to the axis or triangular ones orthogonal to the axis.
 

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