Moment of Inertia in Cylindrical Coordinates

[mathmannn]

Homework Statement

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

Homework Equations

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

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.

 

[tiny-tim]

hi mathmannn!

… my prof said it should be done in polar coordinates. I'm pretty sure that it will come out to be a triple integral …

no, that's crazy , 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