Solve Power-Law Spiral With Angular Momentum L

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To solve for the potential V(r) that results in a spiral path defined by r = C(theta)^k, the relationship between angular momentum L and the time derivative of theta needs to be clarified. The discussion highlights the need to express r' without involving theta, which is essential for integrating it into the energy equation E = K + V(r). Participants explore whether the prime notation in the angular momentum equation indicates a time derivative of theta, suggesting a connection between r and theta-dot. The challenge lies in eliminating r to derive a usable expression that links r and theta. Ultimately, the focus is on finding a suitable form for V(r) that corresponds to the specified trajectory.
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Homework Statement



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

Homework Equations



L = mr2(theta)'

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.
 
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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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