How Do You Calculate the Moment of Inertia of a Cone Using a Triple Integral?

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Homework Help Overview

The discussion revolves around calculating the moment of inertia of a cone using a triple integral, specifically focusing on the axis of rotation being the central axis of the cone.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster seeks assistance in determining the moment of inertia and understanding the volume element (dV) in the context of a triple integral. Some participants suggest looking into cylindrical coordinates for the volume element, while others propose considering the cone as composed of horizontal disks to facilitate integration.

Discussion Status

Participants are exploring various methods to approach the problem, including the use of cylindrical coordinates and the concept of integrating over disks. There is an ongoing exchange of ideas without a clear consensus on a single method.

Contextual Notes

The discussion includes a request for detailed explanations and highlights the need to apply previously learned concepts to this new problem. There may be constraints related to the specifics of the homework assignment that are not fully articulated.

homad2000
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hello,
I need help finding the moment of inertia of a cone using triple integral. can you also explain how can we get dV with details?
 
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the axis of rotation is around the central axis
 
Look up "volume element in cylindrical coordinates". http://keep2.sjfc.edu/faculty/kgreen/vector/Block3/jacob/node9.html" that may help.
 
Last edited by a moderator:
you can even do this ...

consider any horizontal part of cone (that looks like a disk) ... you know moment of inertia of disk ... write it for any disk of radius are and thickness dr ...then integrate it from r=0 to max r

You see there are many ways to find an answer ... just use concepts you learned from the previous questions for new ones !
 

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