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Moment of inertia and rotational kinetic energy

  1. Oct 18, 2012 #1
    I can't seem to understand moment of inertia. What does it mean and how is it derived ?
    How does it relate to rotational kinetic energy.
     
  2. jcsd
  3. Oct 18, 2012 #2

    tiny-tim

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    Hi CrazyNeutrino! :smile:

    From the PF Library on moment of inertia

    Moment of Inertia … relates rotational force (torque) to rotational acceleration in the same way that mass relates ordinary (linear) force to ordinary acceleration.​

    ie τ = Iα just like F = ma

    (and KE = 1/2 Iω2 just like 1/2 mv2)

    it is derived from I = ∫ dm r2
     
  4. Oct 19, 2012 #3
    Why dm r^2?
     
  5. Oct 19, 2012 #4

    tiny-tim

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    because for a point mass m at distance r from the axis, subjected to a force F,

    the torque is τ = Fr, and the angular acceleration is α = a/r

    τ = Iα means Fr = Ia/r

    but F = ma (good ol' Newton's second law)

    so mar = Ia/r

    so I = mr2

    (and moment of inertia of the whole = sum of moments of inertia of the parts, giving us ∫ dm r2)
     
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