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Why can't moment of Inertia be never greater than MR2

  1. Jun 23, 2013 #1
    Why can't moment of Inertia be never greater than MR2 for uniform bodies with simple geometrical shapes?
     
  2. jcsd
  3. Jun 23, 2013 #2

    TSny

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    It's not clear what "R" stands for here. For example, a cube is a simple geometrical shape. What would R be for a cube?
     
  4. Jun 23, 2013 #3
    Apologies. My question was for a condition of friction in Accelerated Pure Rolling of objects like hollow cylinder, solid cylinder, solid sphere, hollow sphere, disc or a ring. So 'R' corresponds to the radius of these objects and 'M' is their mass.
     
  5. Jun 23, 2013 #4
    The moment of inertia is defined to be ## \int_0^R \rho(r) r^2 dV ##. According to the mean value theorem, that is equal to ## \bar{R}^2 \int_0^R \rho(r) dV = \bar{R}^2 M \le R^2 M ##, where ## 0 \le \bar{R} \le R ##.

    Physically, you could think of transporting every bit of mass of an object to its boundary - what would happen with its moment of inertia?
     
  6. Jun 25, 2013 #5

    lalo_u

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    I think it grows up, but i don´t understand what´s the concerning
     
    Last edited: Jun 25, 2013
  7. Jun 25, 2013 #6

    lalo_u

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    I think it grows up, but i don´t understand what´s the concerning
     
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