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Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum.It is an important physical quantity because it is a conserved quantity – the total angular momentum of a closed system remains constant.
For reference and background, two closely related forms of angular momentum are given. In classical mechanics, the orbital angular momentum of a particle with instantaneous three-dimensional position vector x = (x, y, z) and momentum vector p = (p x, p y, p z), is defined as the axial vector = which has three components, that are systematically given by cyclic permutations of Cartesian ...
Conservation of angular momentum states that J for a closed system, or J for the whole universe, is conserved. However, L and S are not generally conserved. For example, the spin–orbit interaction allows angular momentum to transfer back and forth between L and S , with the total J remaining constant.
As an illustration, if a physical system behaves the same regardless of how it is oriented in space (that is, it's invariant), its Lagrangian is symmetric under continuous rotation: from this symmetry, Noether's theorem dictates that the angular momentum of the system be conserved, as a consequence of its laws of motion.
With respect to classical physics, conservation laws include conservation of energy, mass (or matter), linear momentum, angular momentum, and electric charge. With respect to particle physics, particles cannot be created or destroyed except in pairs, where one is ordinary and the other is an antiparticle.
The law of conservation of angular momentum states that in the absence of applied torques, the angular momentum vector is conserved in an inertial reference frame, so =. The angular momentum vector L {\displaystyle \mathbf {L} } can be expressed in terms of the moment of inertia tensor I {\displaystyle \mathbf {I} } and the angular velocity ...
Conservation of angular momentum is the principle that the total angular momentum of a system has a constant magnitude and direction if the system is subjected to no external torque. Angular momentum is a property of a physical system that is a constant of motion (also referred to as a conserved property, time-independent and well-defined) in ...
According to Noether's theorem, if the action (the integral over time of its Lagrangian) of a physical system is invariant under rotation, then angular momentum is conserved. Application to quantum mechanics