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Rotational Inertia

  1. Dec 10, 2012 #1
    Hello,

    I was curious to know if there was some intuitive out-look on why rotational inertia depends on the distance of the mass from the axis of rotation; and why is this distance have to be squared?
     
  2. jcsd
  3. Dec 11, 2012 #2
    Moment of Inertia I = mr2

    Moment of inertia do same work for rotational motion as , inertia for linear motion.

    Since moment of inertia is tendency of body to maintain its initial state of rotation , so it has to depend on distance from axis of rotation also. Remember , torque is force times perpendicular distance of line of action from axis of rotation. As torque depends on the distance "r" , so body's tendency to maintain its rotation has also to depend on distance "r".

    And this distance is squared due to dimensional analysis.

    Let torque T depend on moment of inertia and angular acceleration. (You know it!)

    Equate the dimensions. You'll see that distance has to be squared in moment of inertia.
     
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