Question

Find the components along the x, y, z axes of the angular momentum of a particle, whose position vector is 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-yplane the angular momentum has only a z-component.

Answer 1

we know ,
angular momentum (L) = r x P
where r is the position vector and P is the linear momentum .

a/c to question,
particle moves only in x-y plane .
so,

r = x i + y j

P =Px i +Py j

now,

L = ( x i + yj ) × (Px i + Py j )

=(x.Py k - y.Px k)

=( xPy -y.Px) k

hence, proved that if particle moves in x-y plane then angular momentum of its in z-axis

=

Answer 2

Explanation:

...................