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What exactly is r in inertial equation I=mr^2?

Discussion in 'MCAT Study Question Q&A' started by m25, Sep 4, 2014.

  1. m25

    m25

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    So the general equation for inertia is I=mr^2

    So the distance r represent the distance from the center of rotating axis to exactly what? Center of mass?
     
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  3. Cawolf

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    The point particle of mass m.
     
  4. m25

    m25

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    So what if the mass has a ring-like shape? Would r be from the center of axis to just inside, outside, or right in the middle of the ring?
     
  5. mehc012

    mehc012 Big Damn Hero
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    In that case, technically, the moment of inertia for the entire object would be the sum of the moments of inertia for each point mass which composes the entire ring
    ∑ I1+I2+I3... = ∑ m1r1²+m2r2²+m3r3²...

    Most physics books have a list of equations, somewhere in the rotational motion chapter, which detail the specific equations for finding the overall I of any given shape (assuming uniform density of the material the shape is made of).
    [​IMG]
    [​IMG]
    These equations describe the sum of the moments of inertia for all point masses contained in the object.
     
  6. Cawolf

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    That formula is specifically for a point mass rotating some distance r from the axis of rotation.

    As @mehc012 said, continuous objects are a whole different beast - with integration required to solve for their moment of inertia. I would imagine any continuous object would have it's moment of inertia given on the MCAT.
     
  7. mehc012

    mehc012 Big Damn Hero
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    Or at the very least, an equation similar to those in the above images. My physics prof used to do this to us all the time!
     
  8. Cawolf

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    Yah we had to solve a lot of those problems in physics also - crazy shapes with off center axis that required summing multiple integrals. :thumbdown:
     
  9. m25

    m25

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    Ah, I see. So in the case of point mass, would the distance r be from the axis of rotation to the center of mass of the point mass? Or just outside of the point mass?
     
  10. Cawolf

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    Center of mass.
     
  11. mehc012

    mehc012 Big Damn Hero
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    The center of mass of a point mass...but by definition, a 'point mass' takes up only a single point in space, so r would be the distance to that point.

    You can treat a larger mass as if it is a point mass existing at the center of mass of the larger object.

    I know, it's nitpicky, but it is an important distinction.
     

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