Find the components along the x, y, z axes of the angular momentum l 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 z-component.

Question

Philoid · Accepted Answer

From the given data,

Linear momentum vector,

Position vector,

We have, Angular momentum,

=

∴

By comparing respective components, we get,

Since, the particle moves in x-y plane, then the vectors of both position and linear momentum vectors be Zero.

Thus,

Hence, the particle moves in x-y plane the angular momentum acts towards z-direction.

Find the components along the x, y, z axes of the angular momentum l of a particle, whose position vector is r with components x, y, z and momentum is p with components px, py and pz. Show that if the particle moves only in the x-y plane the angular momentum has only a z-component.