Clarify about the moment of inertia

1. Oct 2, 2011

opeth_35

hey, I want to ask you something about to calculate the moment of inertia for any shape.

My problem is that I can not calculate that moment of inertia values for any shape. Such as

rectangle or stick and the others.

I have tried to calculate for stick and I have found the solution of Ix=∫y2.dm is ∫(L/2)^2dm and after that point how can i calculate dm for this integrnt. I wrote insted of dm which is dm=M/L.dL but I cannot forward within the equation.. ı think there is a very simple thing in this equation but I cannot see that and I cannot solve thıs equatıon properly. I fell like a blind for that.

Please if you help me clarify for that solving i would be appreciate for taht.

2. Oct 2, 2011

Staff: Mentor

Try this:
Ix = ∫x2dm

dm = (M/L)dx

So: Ix = (M/L) ∫x2dx

You should be able to continue the calculation now.

3. Oct 2, 2011

opeth_35

i have a problem again about that solution, Could you check this out again?

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4. Oct 2, 2011

Staff: Mentor

Giving your solution in an attachment makes it more difficult to comment on each step.

Why do you think you need to substitute L/2 for x in the integrand? First do the integration, then substitute the range of variables.

5. Oct 2, 2011

opeth_35

because I have to calculate moment of inertia according to the central axis. thats why I have taken that L/2.

I have been trying to clarify that problem since morning but I still can not. If you say to me how to solve that. Iwill finish that things. please. by the way.. I have tried to solve without putting L/2 first. I found Ix= ML^2 / 24.

Maybe it is so simple to see that here for you, but I cannot. If I bored you sorry! I am just going to second class of my undergraduate.

6. Oct 2, 2011

Staff: Mentor

What you're trying to do is evaluate the definite integral:

$$(M/L)\int_{-L/2}^{+L/2} x^2 dx$$

First find the antiderivative of x^2, then evaluate using the limits of integration.

7. Oct 2, 2011

opeth_35

that has been so clear for me, Thank you for helping me :) my problem was to understand the boundries.. okey..

have a nice days Doc Al:)