Find the components along the $x, y, z$ axes of the angular momentum I of a particle, whose position vector is $r$ with components $x, y, z$ and momentum is $p$ with components $p_{x}, p_{y}$ and $p_{z}$. Show that if the particle moves only in the $x-y$ plane the angular momentum has only a zcomponent.

Home » Find the components along the axes of the angular momentum I of a particle, whose position vector is with components and momentum is with components and . Show that if the particle moves only in the plane the angular momentum has only a zcomponent.

Find the components along the $x, y, z$ axes of the angular momentum I of a particle, whose position vector is $r$ with components $x, y, z$ and momentum is $p$ with components $p_{x}, p_{y}$ and $p_{z}$ . Show that if the particle moves only in the $x-y$ plane the angular momentum has only a zcomponent.

CBSE | Class 11 | NCERT | Physics | System of Particles and Rotational Motion

Find the components along the $x, y, z$ axes of the angular momentum I of a particle, whose position vector is $r$ with components $x, y, z$ and momentum is $p$ with components $p_{x}, p_{y}$ and $p_{z}$ . Show that if the particle moves only in the $x-y$ plane the angular momentum has only a zcomponent.

Linear momentum is given by $\vec{p}=p_{x} \hat{i}+p_{y} \hat{j}+p_{z} \hat{k}$

Positional vector of the body is given by $\vec{r}=x \hat{i}+y \hat{j}+z \hat{k}$

Angular momentum is given by $\vec{I}=\vec{r} \times \vec{p}$

$=(x \hat{i}+y \hat{j}+z \hat{k}) \times\left(p_{x} \hat{i}+p_{y} \hat{j}+p_{z} \hat{k}\right)$

$=\left[\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ x & y & z \\ p_{x} & p_{y} & p_{z}\end{array}\right]=\hat{i}\left(y p_{z}-z p_{y}\right)+\hat{j}\left(z p_{x}-x p_{z}\right)+\hat{k}\left(x p_{y}-y p_{x}\right)$

$l_{x} \hat{i}+l_{y} \hat{j}+l_{z} \hat{k}=\hat{i}\left(y p_{z}-z p_{y}\right)+\hat{j}\left(z p_{x}-x p_{z}\right)+\hat{k}\left(x p_{y}-y p_{x}\right)$