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

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To calculate the moment of inertia of a cone using a triple integral, the focus should be on the volume element in cylindrical coordinates. The axis of rotation is around the cone's central axis, and one can consider horizontal cross-sections of the cone that resemble disks. By determining the moment of inertia for each disk with radius 'r' and thickness 'dr', integration can be performed from r=0 to the maximum radius of the cone. Utilizing previously learned concepts will aid in solving this problem effectively. Understanding these steps is crucial for accurate calculations.
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.
 
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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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