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Question

(A) The angular momentum $\vec{L}$ of a particle with respect to the origin is given by $\vec{L} = \vec{r} 	imes \vec{p} = \vec{r} 	imes (m\vec{v})$

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Variable in magnitude as well as direction

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(A) The angular momentum $\vec{L}$ of a particle with respect to the origin is given by $\vec{L} = \vec{r} 	imes \vec{p} = \vec{r} 	imes (m\vec{v})$.For a particle moving in a circle with uniform speed $v$,the magnitude of angular momentum is $L = mvr_{\perp}$,where $r_{\perp}$ is the perpendicular distance from the origin to the line of velocity. Since the circle is not centered at the origin,the position vector $\vec{r}$ relative to the origin changes continuously as the particle moves along the circle.Consequently,both the magnitude and the direction of the cross product $\vec{r} 	imes \vec{v}$ change as the particle rotates. Therefore,the angular momentum is variable in both magnitude and direction.

$A$ particle is rotating in a circle with uniform speed as shown. The angular momentum of the particle with respect to the origin is .........

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