- #1

Pascal1p

- 28

- 0

## Homework Statement

Determine the moment of inertia of the shaded area about the x axis.[/B]

## Homework Equations

Ix=y^2dA

## The Attempt at a Solution

Okey so I now get how to do this the standard method. But I want to know if the method I tried is correct as well or where my mistake lies.

My attempt:

I look at the portion above x-axis and then multiple it with 2.

So I tried to use the method that I have been taught, a small element that touches the graph like in the picture.

dA= (Rcos (a)- X)dady

since x^2+y^2=R^2, x= sqrt (R^2-y^2)

so I(x)= y^2(Rcos(a)-sqrt (R^2 - y^2))dady

First I integrate this to da with the limits 0 to 1/2a (since the angle goes from 0 to 1/2a)

and then that answer I integrate to dy with limits 0 to Rsin(a/2) (since y goes from 0 to Rsin(a/2)

So basically after the first integration I get:

y^2Rsin(a/2)-(a/2)(y^2)sqrt(R^2-y^2)dy

and then when I integrate this I get this very long and quite complicated equation but is it correct?

I know now the simpler way, but I find it important that I understand it.