Definition:Angular Momentum/Aggregation of Particles

Definition
Let $\PP = \set {P_i: i \in I}$ be an aggregation of particles, indexed by $I$, all in motion relative to a point $O$.

For all $i \in I$, let:
 * the mass of particle $P_i$ be $m_i$
 * the velocity of particle $P_i$ relative to $O$ be $\mathbf v_i$.

The angular momentum of $\PP$ relative to (or about) $O$ is defined as the sum of the angular momenta of each of the particles in $\PP$:


 * $\ds \mathbf L = \sum_{i \mathop \in I} \mathbf r_i \times \mathbf p_i = m \paren {\mathbf r_i \times \mathbf v_i}$

where:
 * $\mathbf p_i$ denotes the (linear) momentum of particle $P_i$ for $i \in I$
 * $\mathbf r_i$ denotes the position vector of particle $P_i$ for $i \in I$ $O$
 * $\times$ denotes the vector cross product.