Angular momentum (classical)

In physics, angular momentum is a kinematic property of one or more point masses. Its importance derives from the fact that it is a conserved quantity in several physical circumstances. (Recall that a conserved quantity of a physical system is a property that does not change over time.)

Point mass m with velocity v has angular momentum L ≡ m r × v with respect to O. L is a vector pointing towards the reader

The angular momentum of a single point mass m is defined with respect to a point O. Denote the vector from O to m by r (see the figure). Let the mass have velocity v, then the angular momentum L of the point mass is the cross product,

$\mathbf {L} \equiv m\mathbf {r} \times \mathbf {v} =\mathbf {r} \times \mathbf {p} .$

It follows from the definition of cross product that the vector L is perpendicular to the plane of the figure and points towards the reader. Note that the definition p ≡ m v for the linear momentum is introduced here.

The definition of the angular momentum of a system of n point masses is the following simple generalization:

$\mathbf {L} _{\mathrm {sys} }\equiv \mathbf {r} _{1}\times \mathbf {p} _{1}+\mathbf {r} _{2}\times \mathbf {p} _{2}+\cdots +\mathbf {r} _{n}\times \mathbf {p} _{n}=\sum _{i=1}^{n}\mathbf {r} _{i}\times \mathbf {p} _{i}.$