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tsw99
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Homework Statement
Moment of inertia of spherical shell of radius R, mass M along its rotation axis is given by [tex]\frac{2}{3}MR^{2}[/tex]
I am trying to calculate this
Homework Equations
The Attempt at a Solution
This is my attempt but is unsuccessful,
since the spherical shell is an assembly of rings (of varying radius), and the MI of a ring is
[tex]I=MR^{2}[/tex]
Hence [tex]dI=y^{2}dm[/tex]
[tex]I=\int y^2(2\pi \sigma ydz[/tex]
Using [tex]y=Rsin\theta[/tex] and [tex]z=Rcos\theta[/tex]
I get:
[tex]I=2 \pi \sigma R^{4} \int sin^{4}\theta d\theta
=2 \pi \sigma R^{4} \frac{3\pi}{8}
=\frac{3\pi MR^{2}}{16}[/tex]
which is incorrect.
Which step I have gone wrong? Thanks
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