# Moment of inertia of a cylinder?

## Homework Statement

the moment of inertia of A cylinder of height 2h radius (a) and uniform mass density ρ about a line x=y=z using multiple integration.

## Homework Equations

I=ρ∫s^2*dV where the integral is over the volume V of cylinder and s is the perpendicular distance to the axis of rotation.

## The Attempt at a Solution

I tried setting s^2=r^2+z^2 and integrate using cylindrical polars with elemental volume dV=rdrdθdz where r from 0 to a, z from -h to h, θ from 0 to 2π But I got the wrong answer.

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gneill
Mentor
Check your assumptions about the distance of the mass element from the axis of rotation. If you're using cylindrical polar coordinates it should simply be the radius coordinate, no Pythagoras involved.

Check your assumptions about the distance of the mass element from the axis of rotation. If you're using cylindrical polar coordinates it should simply be the radius coordinate, no Pythagoras involved.
well, that still is a wrong answer, the thing is the line about which the rotation occurs is not z axis, if it was then yes perpendicular distance is the radius.

gneill
Mentor
well, that still is a wrong answer, the thing is the line about which the rotation occurs is not z axis, if it was then yes perpendicular distance is the radius.
The you'll have to be specific about the orientation of the cylinder and which axis forms the axis of symmetry. Post a sketch if you can, and show us the details of your attempt.