Question

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.

Answer 1

The particle moves in the x-y plane. Hence, the z-component of the position vector
and linear momentum vector becomes zero, i.e., z = p_z = 0

Therefore, when the particle is confined to move in the x-y plane, the direction of angular momentum is along the z-direction.