A particle of mass m moves in the X Y plane with a velocity v along the straight line A B . If the angular momentum of the particle with respect to origin O is L A when it is at A and L B when it is a

Question

A particle of mass m moves in the X Y plane with a velocity v along the straight line A B . If the angular momentum of the particle with respect to origin O is L A when it is at A and L B when it is at B , then

TestHub · Accepted Answer

From the definition of angular momentum,

$L = r \times p = r m v \sin \emptyset (- \hat{k})$

Therefore, the magnitude of $L$ is

$L = m v r \sin \emptyset = m v d$

where $d = r \sin \emptyset$ is the distance of closest approach of the particle to the origin. As $d$ is same for both the particles, hence $L_{A} = L_{B}$ .

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