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Homework Help: Physical interpretation of one of Hamilton's equations

  1. Oct 11, 2012 #1
    1. The problem statement, all variables and given/known data

    I've attached a picture from a passage of my book (Liboff, Quantum Mechanics) with which I am having difficulty. Specifically, equation 1.25 claims to possess a certripetal force factor (in the text underneith) and a moment arm factor. I see both of these terms present. However, shouldn't the centripetal force factor reduce to mv2/r? Also, i assume the moment arm is included because torque is formally (clasically) r x F. However, here θ denotes the polar angle, and so rcos(θ) is the z-component of r. As a result, I dont see how this expression amounts to the torque. Can someone clarify this for me?

    2. Relevant equations

    3. The attempt at a solution

    Attached Files:

  2. jcsd
  3. Oct 11, 2012 #2
    Okay, I may have made some progress already:

    For everything below, phi = σ.

    In this case, mv2/r is equal to m(rσ)2/r = mrσ2. Now, r x F = |r| |F| sin(ζ), where ζ is the angle between r and F. But this must mean here that sin(θ)cos(θ) = sin(ζ), and this is (perhaps?) what I don't see.

    **Upon second thought, this centripetal force arises from motion in the phi direction at constant r and theta, so the cross product is simply the product of the magnitudes r and F (since the angle between these two vectors is always 90 degrees). Thus, disregard my comments above.
    Last edited: Oct 11, 2012
  4. Oct 13, 2012 #3
    Still looking for help!
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