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Math Help - Moment of Inertia

  1. #1
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    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"...
    Last edited by mr fantastic; December 19th 2011 at 04:41 PM. Reason: Title.
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  2. #2
    Super Member ILikeSerena's Avatar
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    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?
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  3. #3
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    Re: [Help] Moment of Inertia

    well if i remember i used:
    x=My/M

    y=Mx/m

    M= integral F(X)dx
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  4. #4
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    Re: [Help] Moment of Inertia

    sorry about my bad english isnt my language! Im from Angola!
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  5. #5
    Super Member ILikeSerena's Avatar
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    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?
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  6. #6
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    Re: [Help] Moment of Inertia

    yeah! where can i draw the graph to put here??
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  7. #7
    Super Member ILikeSerena's Avatar
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    Re: [Help] Moment of Inertia

    To show a graph, you should draw a bitmap and save it for instance as a gif file.
    Above the reply box (in advanced mode) there is a paperclip that allows you to upload.
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  8. #8
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    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
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  9. #9
    Super Member ILikeSerena's Avatar
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    Re: [Help] Moment of Inertia

    Hmm, I guess you have tried to define the boundaries of the area in question.

    Let's start with the boundary given by:
    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?
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  10. #10
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    Re: [Help] Moment of Inertia

    Now i saw i forgot the draw of (x^2)+(y^2)=1
    The other equations are correct??
    Last edited by Ackbeet; December 19th 2011 at 12:13 PM.
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  11. #11
    Super Member ILikeSerena's Avatar
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    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.
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  12. #12
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    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???
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  13. #13
    Super Member ILikeSerena's Avatar
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    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)!
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  14. #14
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    Re: [Help] Moment of Inertia

    Does not the forum have a chat?
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  15. #15
    Super Member ILikeSerena's Avatar
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    Re: [Help] Moment of Inertia

    Probably, but I haven't been there yet.
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