Angular Momentum

Angular momentum in classical mechanics

Definition

The angular momentum L of a particle about a given origin is defined as:

 

where r is the position vector of the particle relative to the origin, p is the linear momentum of the particle, and × denotes the cross product.

As seen from the definition, the derived SI units of angular momentum are newton metre seconds (N·m·s or kg·m²s⁻¹) or joule seconds. Because of the cross product, L is a pseudovector perpendicular to both the radial vector r and the momentum vector p and it is assigned a sign by the right-hand rule.

For an object with a fixed mass that is rotating about a fixed symmetry axis, the angular momentum is expressed as the product of the moment of inertia of the object and its angular velocity vector:

where I is the moment of inertia of the object (in general, a tensor quantity), and ω is the angular velocity.

Angular momentum is also known as moment of momentum.