Explain Cartesian components of angular momentum of a particle.
Explain Cartesian components of angular momentum of a particle.
By definition of angular momentum
$\vec{l}=\vec{r} \times \vec{p}$
$\hat{i}\hat{j}\hat{k}$
$x\;y\;z$
$\mathrm{P}_{x}\mathrm{P}_{y}\mathrm{P}_{z}$
$=\hat{i}[y \mathrm{P} z-z \mathrm{P} y]+\hat{j}[z \mathrm{P} x-x \mathrm{P} z]+\hat{k}[x \mathrm{P} y-y \mathrm{P} x] \ldots \ldots . .(1)$
$\therefore \vec{l}=l_{x} \hat{i}+l_{y} \hat{j}+l_{z} \hat{k}$
Here $l_{x}, l_{y}$ and $l_{z}$ are the components of $\vec{l}$ along $\mathrm{X}, \mathrm{Y}$ and $Z$ axis respectively.
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