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Math Help - Center of Mass and Density

  1. #1
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    Center of Mass and Density

    Hello my class has been talking about centers of mass, centroids, and density the last couple of days and instructor told us to come up with an argument to the following statement, If you have a plate with density delta and finite area does it have a center of mass?
    He told us to consider a ring where it would have a definite density and area but no center of mass. When I was thinking about this I was wondering if you could just spin it on its y axis and balance it upright. Anyways any ideas or suggestions that would help add to my input would be appreciated.
    Thanks.
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  2. #2
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    Re: Center of Mass and Density

    I am not sure exactly what you are saying. Any object with finite volume and density functions has a "center of mass" but it is not necessarily in the object itself. For example, if the object is a uniform ring, then the center of mass is, by symmetry, at the center of the ring.
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  3. #3
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    Re: Center of Mass and Density

    How can the center of mass of an object exist outside of an object? I understand that in your example the object happens to be a ring which has no material center, but in that case how can you consider the center of mass to exist where no material exists? Do you understand what my question is asking?
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  4. #4
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    Re: Center of Mass and Density

    Do YOU understand what "center of mass" means? In your class discussion, what definition of "center of mass" did you use? Where in that definition does it say anything about the center of mass of an object being in the mass itself?
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