[Physics] The subtle differences between angular momentum and centrifugal force

angular momentumcentrifugal forcenewtonian-mechanicsreference framesvectors

I am a mathematician wanting to understand the differences between the concepts of angular momentum and centrifugal force.

The following two ideas are clear to me from a physical point of view, but I have a difficult time discerning the difference between them as people tell me they are different but do not give me any explicit reason as to why.

  1. Angular momentum is a vector quantity (taken in the physical sense) of a mass's rotational velocity about some axis.

  2. Centrifugal force is defined on the axis of a rotational reference frame, which depends on the inertia of the object.

My question: What is the subtle difference between this notion of "rotational reference frame" and the notion of the vector quantity of a mass's rotational velocity?. Are they not physically the same point (vector quantity) of rotation about an axis, thus making the meaning of centrifugal force a relative way to speak about the meaning of angular momentum?

I hope this question isn't too naive. I have been really hoping to understand the subtle difference between these physical concepts in a straightforward way.

Best Answer

I can't quite fathom the source of your confusion (I think it might have something to do with a focus on the notion of rotation here---angular momentum does not require rotational motion), so I'm having trouble writing a really clear response. For the moment I would rather offer a program for practicing the right skills rather than reinforcing the mistaken thinking.

  1. Stop trying to do physics is non-inertial frames until you are totally comfortable doing physics in inertia frames. That means there is no centrifugal (pseudo-)force, only a centripetal component to the forces acting on the body.

  2. Work a lot with angular momentum, get used to the idea that you get the same physics from it no matter what point you chose as the "axis" (though the values of $L$ and $I$ change) and that you can chose a notional axis that does not correspond to a physical pivot.

  3. When you start again with non-inertial reference frames do a non-rotating one first. Get used to the idea that pseudo-forces emerge from using a "wrong" coordinate system and that you can get the results in a "right" coordinate system instead.

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