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I Exactly why are these two expressions similar?

  1. Aug 22, 2016 #1
    So if angular momentum

    [itex]

    L = m r^2 \dot {\theta}

    [/itex]

    and we take the first time derivative

    [itex]

    \frac {d}{dt} L = 2mr \dot {r} \dot {\theta} + m r^2 \ddot {\theta}

    [/itex]

    the first term looks similar to the Coriolis force [itex] 2m( \bf {v} x \bf { \dot {\theta} } ) [/itex]
    but I can't figure out why. Of course they both have to do with rotation so I'm guessing that it's not a coincidence, but I can't quite arrive at the exact mathematical connection between the two expressions.

    Would anyone like to help me out?
     
  2. jcsd
  3. Aug 22, 2016 #2

    mfb

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    2016 Award

    Staff: Mentor

    Doesn't look similar to me. Cross product vs. no cross product, and then you have the additional radius in one equation.
     
  4. Aug 22, 2016 #3
    Yes, I should have expressed angular momentum and its time derivative as vectors as well, then we'd have cross products on both sides.

    For the moment my hunch reasoning goes like this:

    1.) In a rotating frame of reference, a "floating by" object (one not acted on by external forces) is subject to two fictious forces — centrifugal and Coriolis.

    2.) A force causes a change in (linear) momentum.

    3.) Angular momentum is a function of linear momentum, therefore a change in one is likely to effect a change in the other.

    4.) The time derivative of angular momentum expresses a change in angular momentum.

    So there's a connection. Hopefully this is enough to lead me through the mathematics and see if the similarity of the two terms mentioned in the OP is a coincidence or not.
     
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