I was once criticized for "taking angular momentum as momentum going in a circle". I was loosely trying to state, in classical mechanics, that in using conservation of momentum, one can switch between linear and angular momentum, in a problem when one is not concerned with rotation of the body on itself, and even treat rotational motion with linear momentum. I think that, in a very real sense, angular momentum can also be seen as momentum going in a circle. This is because circular motion can be seen as velocity going in a circle, meaning of course that its direction changes to stay tangential, even though there are other more abstract formulations or formalizations with a different dimentionality.
Actually I realize that this is hardly a physics problem, but rather pure kinematics. Very simply because when considering only linear (not necessarily straight) motion of a mass, one can simply factor out the mass and deal with speed and acceleration, rather than momentum and forces.
The idea is that the speed (momentum magnitude) of a body (mass) is constant when all accelerations (forces) are orthogonal to the trajectory, whatever the shape of that trajectory.
This does not seem too original.
It provides a very simple treatment of some single body (angular) momentum conservation problem, but no one seem to ever use it.
It is particularly useful if one has to analyze strange trajectories, for example imposed by rails.
Of course, it can be extended to the case of non-orthogonal accelerations (forces) by projecting the acceleration (force) on the trajectory tangent to get the speed (momentum magnitude) variation.
So I would like to know the proper mathematical formulation of this, or a web reference where this is discussed and formulated mathematically, especially in the case of non orthogonal forces. I could not find it myself, but it may be a question of having the right keywords.
I am also curious as to why this seems not much considered in practice. I feel it gives beginners or amateurs a wrong perception of momentum conservation laws which are much more interesting when used to analyze interactions between parts of a system. Dynamics with a single mass is hardly dynamics.