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Power-law spiral

  1. Mar 10, 2009 #1
    1. The problem statement, all variables and given/known data

    Given L (angular momentum), find the form of V (r) so that the path of a particle is given by the spiral r = C(theta)k, where C and k are constants

    2. Relevant equations

    L = mr2(theta)'

    3. The attempt at a solution

    I know I have to find a expression for r' using no theta's and insert it into the energy formula E = K + V(r) but I am lost on how to apply it.
  2. jcsd
  3. Mar 10, 2009 #2
    Is that prime you have written on theta' in the angular momentum expression the time derivative of theta?

    If so, doesn't that give you a relation between r and theta-dot?
    The required trajectory is a relation between r and theta. Could you eliminate r between these two and do anything with that?
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