Angular Momentum
Angular momentum is the rotational counterpart of linear momentum: for a point mass it is L = r × p, the cross product of the position vector with the momentum. It is conserved whenever the forces acting are central — directed along the line joining the bodies — and, more generally, whenever the physics is invariant under rotation.
The standard account
Conservation of angular momentum is the rotational case of Noether's theorem: rotational symmetry of the laws implies a conserved quantity, and that quantity is angular momentum. Kepler's second law, that a planet sweeps equal areas in equal times, is nothing other than the conservation of angular momentum for a central force, and was empirical eighty years before Newton supplied the reason.
In quantum mechanics angular momentum is quantized in units of the reduced Planck constant ℏ. Orbital angular momentum takes integer multiples; intrinsic angular momentum — spin — takes half-integer multiples for fermions and integer for bosons. The Stern–Gerlach experiment of 1922 demonstrated the space quantization directly. Light carries angular momentum too: Beth measured the torque exerted by circularly polarized light on a suspended waveplate in 1936, and orbital angular momentum of light is now routinely engineered in beams with helical wavefronts.
Angular momentum is the organizing quantity of astrophysics. It is why accretion discs form rather than direct infall, why collapsing clouds spin up, and why the shape of the Solar System is what it is. It is also the source of one of the older acknowledged puzzles in the subject: the Sun holds the overwhelming majority of the Solar System's mass but only a small fraction of its angular momentum, most of which resides in Jupiter and the outer planets. Magnetic braking and disc transport are the standard explanations; they are plausible and incompletely verified.
On this wiki
Angular momentum functions here as a hub, because several distinct programmes in this collection converge on it.
Angular momentum as the primitive, in place of force. Vivian Pope argued that angular momentum, not force, should be taken as the basic dynamical quantity, and attempted to derive gravitational and electrostatic interaction from it in "An Angular Momentum Synthesis of Gravitational and Electrostatic Forces" and "The Angular Momentum Aether". This is a genuinely different starting point rather than a modification of the standard one.
Kepler's second law and what it does and does not imply. Pari Spolter's "Kepler's Second Law and Conservation of Angular Momentum" is part of her wider argument that gravitational force is not proportional to the mass of the attracted body. The second law itself is common ground; what she disputes is what is read into it.
Spin as literal rotation. The Toroidal Ring tradition — Parson's magneton as developed by David L Bergman and Charles William Lucas in Common Sense Science — treats particle spin as the actual rotation of an actual extended object, so that the electron's magnetic moment follows from circulating charge rather than from an abstract quantum number. This is one of the sharpest points of contrast between the models catalogued here and standard quantum mechanics, in which the electron's "spin" is explicitly not a rotation of anything. See Electric Charge for the related derivations of charge from structure.
Conservation questioned. Stefan Marinov claimed experimental violation in "Violation of the Laws of Conservation of Angular Momentum and Energy", and Philipp M Kanarev reworks the conservation law itself in "The Law of Conservation of Angular Momentum". Claims of violation should be treated with the caution they invite: angular momentum conservation follows from rotational symmetry, so a real violation would be a very large result, and no such claim in this collection has been independently reproduced. Related material appears in the over-unity literature here — see Jovan Marjanovic's "Angular Momentum, Parametric Oscillator and Over Unity" and "The Problem of Conservation of Mass-Energy and Angular Momentum by an Elastic Torus with Angular Acceleration" — and belongs to the New Energy thread rather than to the mechanics.
Cosmological angular momentum. Billie Westergard treats it as a structural feature of a universe model in "Degenerate Angular Momentum in the Hotson-Westergard Universe Model".