Definition:Angular Momentum/Particle
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Definition
Let $P$ be a particle of mass $m$ moving with velocity $\mathbf v$ relative to a point $O$.
The angular momentum of $P$ relative to (or about) $O$ is defined as:
- $\mathbf L = \mathbf r \times \mathbf p = m \paren {\mathbf r \times \mathbf v}$
where:
- $\mathbf p$ denotes the (linear) momentum of $P$
- $\mathbf r$ denotes the position vector of $P$ with respect to $O$
- $\times$ denotes the vector cross product.
Also presented as
Some sources present the definition of the angular momentum of a particle $P$ relative to a point $A$ as:
- $\mathbf L = \paren {\mathbf r - \mathbf r_A} \times m \mathbf v$
where:
- $m$ denotes the mass of $P$
- $\mathbf v$ velocity of $P$ relative to the frame of reference in which the motion of $P$ is defined
- $\mathbf r$ denotes the position vector of $P$
- $\mathbf r_A$ denotes the position vector of $A$
- $\times$ 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)
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): angular momentum