Definition:Angular Momentum/Aggregation of Particles
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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 $i \in I$ with respect to $O$
- $\times$ denotes the vector cross product.
Also see
- Results about angular momentum can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): angular momentum (moment of momentum)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): angular momentum (moment of momentum)