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Homework Help: Center of mass and Moment of Intertia

  1. Apr 4, 2010 #1
    1. The problem statement, all variables and given/known data
    The thickness of the object is 2 cm. The density of the material (pronounced row) is 7800. The angle (theta) is pi/6. The radius is .75 meters. What is the moment of inertia and
    the center of mass?

    Here is what the object looks like:


    The object is rotating around the origin.

    2. Relevant equations
    None given

    3. The attempt at a solution
    Okay, so I have no idea how to find the center of mass for this object. I know you have to use integration, but the other kid in my class was using triple integration (which is something I don't know and I don't know if he was right any way). So I have no idea how to find the center of mass for this object.

    As for the moment of inertia, I think that the moment of inertia will be 1/12 of the moment of inertia of a cylinder. I figure this because pi/6 = 30 degrees. 360/30=12. So I think that the moment of inertia will be:

    I= 1/2m[(r1^2)+(r2^2)] * 1/12

    this is just the moment of inertia formula for a hollow cylinder and I multiplied it by 1/12.

    Thank you very much for helping me in any way!!!
  2. jcsd
  3. Apr 4, 2010 #2


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    Homework Helper

    You don't need triple integration. Instead of using x,y,z coordinates, use "r" instead. You can integrate dm*r, then divide the result by the mass to get the r coordinate of the center of mass.

    That's not right. Think about it this way: if we fill in the missing 11/12 of the cylinder, the cylinder's mass would be 12m.
  4. Apr 4, 2010 #3
    Oh thank you!

    But, I don't really understand how to find the moment of inertia and now I don't know how to find the center of mass. Can you show me how to find it for this problem? I have no idea what dm is.
  5. Apr 5, 2010 #4

    anyone know how to solve this?
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