# Very basic moment of inertia question

• Mar 5th 2013, 08:25 PM
togo
Very basic moment of inertia question
26-5-7

Find the moment of inertia of a plate covering the region bounded by x = -1, x = 1, y = 0 and y= 1 with respect to x axis.

Basic equation
Ix = k integral (x^2 * y)
x^2 * 1
= x^2
Integrate x^2:
1/3x^3

so the answer is k * 1/3x^3
and we would plug 1 into x?

the book answer is 2/3k... any hints? thanks.
• Mar 6th 2013, 06:38 AM
hollywood
Re: Very basic moment of inertia question
I think you have an extra y in the basic equation - it should be $\displaystyle I_x=k\int\int x^2\,dx\,dy =k\int_{-1}^1x^2\,dx =\frac{2}{3}k$.

- Hollywood
• Mar 6th 2013, 08:15 AM
togo
Re: Very basic moment of inertia question
sorry still not understanding how you got 2/3k in the end
• Mar 6th 2013, 04:41 PM
hollywood
Re: Very basic moment of inertia question
Here's how I did the last step:

$\displaystyle k\int_{-1}^1x^2\,dx =k\left[\frac{x^3}{3} \right]_{-1}^1 =$

$\displaystyle k\left( \frac{(1)^3}{3}-\frac{(-1)^3}{3} \right) = k\left( \frac{1}{3} - \frac{-1}{3} \right)= \frac{2}{3}k.$

- Hollywood