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Moment of force

  1. Jan 11, 2012 #1
    The way that I can understand how torque works is to say that the greater distance from the rotation axis that you apply your force, the greater power you are delivering to your object - since the farther you are away from the rotational centre the faster something is moving on your rotating object.
    But the way my book derives the relationship
    (1) Ʃτ = Iα
    is kind of mysterious to me, as I don't see where my interpretation shows up during the steps.
    They say let F be a force applied to the object. Every i'th particle will experience an acceleration such, that the angular velocity is the same for our rigid body. We thus have:
    Fi = mi * a = mi * r * α
    And multiplying with r yields:
    τi = mi * r^2 * α
    And summing over all torques gives us (1) - i.e. the rotational analogue of Newtons 2nd law. All there is left to show is then that the internal torques add to zero, but that's simple. I just don't see where the energy interpretation appears in this derivation - can someone open my eyes? :)
     
  2. jcsd
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