Category:Definitions/Angular Momentum
This category contains definitions related to Angular Momentum.
Related results can be found in Category:Angular Momentum.
Particle
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.
Aggregation of Particles
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.
Rigid Body
The angular momentum of a rigid body about a point $O$ is the vector cross product of its moment of inertia $\mathbf I$ about $O$ by its angular velocity $\omega$ about $O$:
- $\mathbf L = \mathbf I \times \omega$
Subcategories
This category has the following 2 subcategories, out of 2 total.
Pages in category "Definitions/Angular Momentum"
The following 15 pages are in this category, out of 15 total.
A
- Definition:Angular Momentum
- Definition:Angular Momentum of Aggregation of Particles
- Definition:Angular Momentum of Particle
- Definition:Angular Momentum of Particle/Also presented as
- Definition:Angular Momentum of Rigid Body
- Definition:Angular Momentum/Aggregation of Particles
- Definition:Angular Momentum/Also known as
- Definition:Angular Momentum/Dimension
- Definition:Angular Momentum/Particle
- Definition:Angular Momentum/Rigid Body
- Definition:Angular Momentum/Symbol