# Moment of inertia of a lamina

1. Oct 2, 2009

### longrob

1. The problem statement, all variables and given/known data
A lamina of unit density consists of the region between the two curves $$y=\sqrt{4-x^2}$$ and $$y=1-4x^2$$ and the x axis.
Find it's moment of inertia about the x-axis.

2. Relevant equations
$$2\left \{ \int_{0}^{2}\int_{0}^{\sqrt{4-x^2}}}y^2 dy dx - \int_{0}^{1/2}\int_{0}^{1-4x^2}y^2 dy dx \right \}$$
which I do understand.

3. The attempt at a solution
$$2\int_{0}^{2}\int_{1-4x^2}^{\sqrt{4-x^2}}y^2 dy dx$$
I don't understand why this is wrong.

2. Oct 2, 2009

### Dick

Because you only want the moment of inertia BETWEEN the two curves. 1-4x^2 is negative for x>1/2. Sketch a graph of the region you want. You have to split the integral into two parts.

3. Oct 2, 2009

### longrob

Thank you. That makes perfect sense !!