# Dynamics, moment of inertia

1. Apr 1, 2012

### mathmannn

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

What is the mass moment of inertia about the y-axis of the object shown if the density is 4 slugs/ft3?

2. Relevant equations

$I_y = \int (x^2 + z^2) dm$
$dm = \rho dV$

3. The attempt at a solution
Not really too sure how to set this one up, my prof said it should be done in polar coordinates. I'm pretty sure that it will come out to be a triple integral but it's been a while since I've done those and could use a little help setting this up.

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2. Apr 2, 2012

### tiny-tim

hi mathmannn!
no, that's crazy :yuck:, it should obviously be cylindrical coordinates

slice the region into vertical cylindrical shells of thickness dr (finding the volume and moment of inertia of each shell is elementary), and then you only have a single integral, over r