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 with components and . Show that if the particle moves only in the x-y plane the angular momentum has only a z-component.
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Text solutionVerified
Linear momentum of particle,
Thus when particle is confined to move in the x-y plane, the angular momentum of particle is along the z-direction.
Position vector of the particle,
Angular momentum,
Therefore on comparison of coefficients,
The particle moves in the x-y plane. Hence the z component of the position vector and linear momentum vector becomes zero.
Thus
Thus when particle is confined to move in the x-y plane, the angular momentum of particle is along the z-direction.
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Question Text | 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 with components and . Show that if the particle moves only in the x-y plane the angular momentum has only a z-component. |
Answer Type | Text solution:1 |
Upvotes | 151 |