(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Moment of Intertia of Spherical Cap?

1. The problem statement, all variables and given/known data

I am having some serious trouble trying to setup this problem..

Find the rotational intertia about the z axis of a spherical cap cut from the sphere [tex]x^2[/tex]+[tex]y^2[/tex]+[tex]z^2[/tex]=4 by the horizontal plane z=1.

2. Relevant equations

Suggestions for solving the problem:

[tex]I\check{z}[/tex]= [tex]\int[/tex] [tex]\rho[/tex] [tex]r^2[/tex] dV

where [tex]\rho[/tex]=[tex]1/r[/tex]

3. The attempt at a solution

I found this thread: /showthread.php?t=78673

Can't post URL's till after 15 posts but it's there.

Here is the suggestion from this this thread:

[tex]I = \frac{1}{2}\rho\pi(\int_{z_0}^R R^4 dz -\int_{z_0}^R 2R^2z^2dz + \int_{z_0}^R z^4dz)[/tex]

Is this the idea I should be following? Or is there a different method to calculating my problem?

It seems my book wants me to go with a triple integration, so here is how I have been trying to do it:

[tex]I = \frac{1}{r} \int_{z= 1}^h\int_{r= 0}^q\int_{\theta=0}^{2\pi}} r dr d\theta dz[/itex]

where q=\sqrt{4-z^2}

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# Homework Help: Moment of Intertia of Spherical Cap?

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