- #1

- 1,097

- 3

## Homework Statement

A plate with constant mass per unit area [tex]\rho[/tex] is bounded by the curve [tex](x^{2} +y^{2})^{2} = 9(x^{2} - y^{2})[/tex] . Find its moment of inertia about the x-axis.

## Homework Equations

## The Attempt at a Solution

Okay well first I plugged in,

[tex]x=rcos\theta,y=rsin\theta[/tex]

into my equation and simplified a little giving me the following result,

[tex]r^{2} = 9cos(2\theta)[/tex]

Now I know the moment of inertia about the x-axis is defined to be,

[tex]\int \int_{R} y^{2} \rho dA[/tex]

Now if I want to consider this in polar coordinates would it simply be,

[tex]\int^{\beta}_{\alpha} \int^{r_{2}}_{r_{1}} r^{2}sin^{2}\theta \rho rdrd\theta[/tex]

I'm a little confused on how the bounding curve plays into this problem.

Any help?