# Moment of Inertia

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• Dec 18th 2011, 08:27 AM
Chipset3600
Moment of Inertia
Please i did this exercice in a Math test and i want you guys to help me know if my result is correct...
Exercice:
Calculate the moment of inertia about the origin of a uniform plate of mass M and such that:
${y}^{2}+{x}^{2}\leq1\wedge0 \leq x \leq y \wedge x + y \geq 1$

My result was "I=0"...
• Dec 18th 2011, 09:48 AM
ILikeSerena
Re: [Help] Moment of Inertia
Welcome to MHF, Chipset3600! :)

I'm afraid your result is not correct.
A moment of inertia of any mass is never zero.

Which formula did you use to calculate it?
• Dec 18th 2011, 10:03 AM
Chipset3600
Re: [Help] Moment of Inertia
well if i remember i used:
x=My/M

y=Mx/m

M= integral F(X)dx
• Dec 18th 2011, 10:04 AM
Chipset3600
Re: [Help] Moment of Inertia
• Dec 18th 2011, 10:14 AM
ILikeSerena
Re: [Help] Moment of Inertia
Erm... that is not the formula for moment of inertia I'm afraid... I'm not sure what it is...
What is M? And m? and F(x)?

The moment of inertia is given by:
$I ~\overset{def}{=}~ \int \int_M r^2 dm$
where the integrals are taken over the relevant area of mass M, r is the distance to the origin, and dm is an infinitesimal amount of mass.

Do you know how to evaluate such an integral over the area given to you?
• Dec 18th 2011, 10:25 AM
Chipset3600
Re: [Help] Moment of Inertia
yeah! where can i draw the graph to put here??
• Dec 18th 2011, 10:34 AM
ILikeSerena
Re: [Help] Moment of Inertia
To show a graph, you should draw a bitmap and save it for instance as a gif file.
• Dec 18th 2011, 10:59 AM
Chipset3600
Re: [Help] Moment of Inertia
my graph was something like this: http://i.imgur.com/tso7y.jpg
Guess i have many thing to study :(
im not good in integrals and area yet
• Dec 18th 2011, 11:23 AM
ILikeSerena
Re: [Help] Moment of Inertia
Hmm, I guess you have tried to define the boundaries of the area in question.

$x^2+y^2 \le 1$
This is an inequality that defines a circular disk of radius 1.

However, I do not see that in your drawing.
Or am I misunderstanding?
• Dec 18th 2011, 11:27 AM
Chipset3600
Re: [Help] Moment of Inertia
Now i saw i forgot the draw of (x^2)+(y^2)=1
The other equations are correct??
• Dec 18th 2011, 11:42 AM
ILikeSerena
Re: [Help] Moment of Inertia
Well, you drew more lines than I would expect... but I'm missing $x+y \ge 1$ for certain.
And it would help if you would shade the part that you think is the actual area.
• Dec 18th 2011, 11:49 AM
Chipset3600
Re: [Help] Moment of Inertia
Thank you for the atention! Is my first time in a mathematic forum, now ill gonna stay in the forum with you guys, learning and help with i can...:)
Did you have a indicate material for a beginner in "Calculus" like me???
• Dec 18th 2011, 11:55 AM
ILikeSerena
Re: [Help] Moment of Inertia
You're welcome! :)

But as it is, I don't know.
I'm a newbie myself on this forum (this is my 2nd day)! ;)
• Dec 18th 2011, 12:10 PM
Chipset3600
Re: [Help] Moment of Inertia
Does not the forum have a chat?
• Dec 18th 2011, 12:13 PM
ILikeSerena
Re: [Help] Moment of Inertia
Probably, but I haven't been there yet.
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