Moment of inertia, Sphere. New method.

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Homework Help Overview

The discussion revolves around the moment of inertia of a solid sphere, specifically seeking various methods to derive the formula \( \frac{2}{5}mR^2 \). Participants are exploring different approaches, including calculus-based methods and experimental techniques.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are discussing multiple methods to calculate the moment of inertia, with mentions of calculus approaches involving disks, spheres, and shells. There is curiosity about the differences between the methods and the potential for new ideas.

Discussion Status

The discussion is active, with participants sharing their knowledge of existing methods and expressing interest in discovering new approaches. There is a focus on understanding the variations in methods and the reasoning behind them.

Contextual Notes

Participants are operating under the premise that there are numerous methods to derive the moment of inertia, with some uncertainty about the exact number and types of methods available. The original poster is specifically looking for innovative ideas beyond the known methods.

jaeoos
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Q. Show the moment of inertia of sphere is 2/5mR^2
using many different methods.

My professor said he knew 18 different method.
Do you have a new idea?
Tell me anything you know. I hope one of your methods will be the 19th method.
 
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Perhaps your professor was referring to experimental methods of finding moment of inertia of a solid sphere ( I am sure there are more than 18).
The only method, by way of proof, that I know of involves calculus.
 
I have found 4 methods involving calculus.
calculus from disk(2 methods), sphere and shell.
 
Your two methods using discs, how do they vary ?
Also I would like to know your approach using a sphere .
 

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