Answered: trying to calculate the moment of…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

I'm trying to calculate the moment of inertia of a sphere. When I calculate moment of inertia by using dI of a small disk (dI=1/2dmy^2) I have a different answer with when I calculate it through expression I=integral(r^2dm). I have two different answers. Why integral method (the second picture) doesn't work ?

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but why we cant use formula I=integral(r^2dm) directly and get the same result? we can choose a small element dm=p(piy^2)dz and yet the answer is different. I cant understand the reason why

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