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Is this a correct derivation of Moment of Inertia?

  1. Jul 21, 2013 #1
    Hello everybody!
    This is the derivation (for a single particle).
    [tex]
    \tau = F_{\perp }r
    \ = ma_{\perp}r
    \ = \alpha mr^2 \\
    \text{if }\
    \tau = I\alpha
    \text{ where } I \text{ is resistance to accleration then } \\
    I = mr^2
    [/tex]
    I'm curious what the problem with this is because I haven't seen it in any of my physics texts (serway and university at least). I also haven't seen it on the interwebs very much.
    Thanks for reading.
     
  2. jcsd
  3. Jul 21, 2013 #2

    Andrew Mason

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    Homework Helper

    Moment of inertia refers to the ratio of the torque to angular acceleration of a rigid body about an axis. It is the inertial resistance to rotation that a rigid body has about a specific axis of rotation. A single particle is not a rigid body.

    What you are doing is determining the ratio of torque to angular acceleration of a single point particle about an axis of rotation.

    If you were to reduce a rigid body to a collection of single point particles of mass dm and add up all the dmr2 terms where r is the distance from the point particle to the axis of rotation, you would end up with the moment of inertia of the rigid body.

    AM
     
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