Rotational Dynamics
2.0 Angular momentum or moment of a momentum
2.0 Angular momentum or moment of a momentum
Angular momentum of a particle about a given axis is the moment of linear momentum of the particle about that axis.
It is denoted by the symbol $\overrightarrow L $
Mathematically, $$\begin{equation} \begin{aligned} \overrightarrow L = \overrightarrow r \times \overrightarrow p \\ \overrightarrow L = m\left( {\overrightarrow r \times \overrightarrow v } \right) \\\end{aligned} \end{equation} $$
Magnitude of an angular momentum is given as, $$\begin{equation} \begin{aligned} \left| {\overrightarrow L } \right| = rp\sin \theta \\ \left| {\overrightarrow L } \right| = mvr\sin \theta \\\end{aligned} \end{equation} $$
where,
$\overrightarrow L $: is the angular momentum of a particle about a given point $O$
$\overrightarrow r $: position vector of the particle with respect to a given point $O$
$\overrightarrow p $: linear momentum of the particle with respect to a given point $O$
Note:
- Angular momentum is a vector quantity
- Its SI unit is $kg - {m^2}/s$
- Its dimensional formula is $\left[ {{M^1}{L^2}{T^{ - 1}}} \right]$
- Direction of the angular momentum is determined by the right hand thumb rule
- By convention angular momentum in the anti-clock wise direction is taken as positiv
- angular momentum in the anti-clock wise direction is taken as negative
- It is not necessary for a body to rotate to have angular momentum
- A body undergoing translation motion also have angular momentum
- Angular momentum depends on the point about which it is calculated
