Q. 64.1( 11 Votes )

# 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 :

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.

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