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

Question

A particle of mass m moves in the XY plane with a velocity v along the straight line AB . If the angular momentum of the particle with respect to the 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,

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

Therefore, the magnitude of $L$ is

$L = m v r \sin ϕ = m v d$

where $d = r \sin ϕ$ 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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