Definition:Angular Momentum/Particle

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