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Weird second law of newton for rotation

  1. Dec 12, 2009 #1
    the proof of second law of newton for rotation goes like this:
    take a sphere rotating around some far axis
    FT=maT
    FT=m * ALPHA * R
    multiple by R

    tau = mR2 * ALPHA

    and we can say it true for every limit mass in a body.
    so

    sigma tau = sigma (mR2) * ALPHA
    sigma tau = I * ALPHA

    internal torque=0
    thus, sigma tau = sigma external tau

    fine, i get it, i think.


    but what if we didn't multiple by R?
    let's return to here
    FT=m * ALPHA * R

    and do not multiple by R

    now as far as i see it, this is also true for every limit mass on a body, so
    sigma FT = sigma (mr) * ALPHA
    internal forces=0 (?)
    thus
    sigma external FT = FT = sigma (mr) * ALPHA

    but that just doest make sense... since it as though it doesn't matter where the force is applied...


    thanks a lot for helping....
     
  2. jcsd
  3. Dec 12, 2009 #2
    What do you mean by "it doesn't matter..."?
    In any case you have to keep in mind that you had vector quantities before. For example one could use a vector [itex]\vec{R}[/itex] which had length R, but direction perpendicular to the displacement and into the direction of the acceleration. Then your equation would be
    [tex]\sum_i \vec{F_i}=\sum_i (m_i\vec{R}_i(t))\cdot\alpha[/tex]
    which due to the time dependence is not very helpful.
     
  4. Dec 12, 2009 #3
    by "it doesn't matters" i simply mean that, wherever the force is exerts relative to the axis, it'll cause the same angular acceleration, which we know not to be true..

    and i didn't quite get it... where the time came from?
     
  5. Dec 12, 2009 #4
    The point is that you need to use exact notation, which encompasses using vectors for the force (otherwise the sum of the forces is not equal to the total external force!).
    The time dependence is since the orientation and thus R will change with time.
     
  6. Dec 16, 2009 #5
    wow... i still don't get it...
    can you write to me the real proof of torque? so i can see how it should be done?
    thanks
     
  7. Dec 16, 2009 #6
    Have a look at
    https://www.physicsforums.com/showthread.php?t=363521
    It's not the full answer to your question, but feel free to request a special answer :)

    There I explain how the general torque law derives for a set of particle.
    If the particles form a rigid body, then the proof can be continued. I think about what you would like to hear and some time later I make a post.
     
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