A particle of mass m moves with a velocity v | vedclass

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Question

(B) The angular momentum $L$ of a particle about a point $O$ is defined as the cross product of its position vector $\vec{r}$ and its linear momentum

Vedclass · Accepted Answer

$mvl$

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(B) The angular momentum $L$ of a particle about a point $O$ is defined as the cross product of its position vector $\vec{r}$ and its linear momentum $\vec{p} = m\vec{v}$.Mathematically,$\vec{L} = \vec{r} 	imes \vec{p} = \vec{r} 	imes (m\vec{v})$.The magnitude of angular momentum is given by $L = mvr \sin 	heta$,where $	heta$ is the angle between the position vector $\vec{r}$ and the velocity vector $\vec{v}$.Alternatively,the magnitude of angular momentum can be expressed as the product of the linear momentum $(mv)$ and the perpendicular distance $(l)$ from the point of rotation $(O)$ to the line of action of the linear momentum.Therefore,the angular momentum about point $O$ is $L = mv 	imes l$.

$A$ particle of mass $m$ moves with a velocity $v$ along the line $PC$ (as shown in the figure). The angular momentum of the particle about point $O$ is:

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