A small mass m is attached to a massless stri | vedclass

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Question

(C) The angular momentum about a point is given by $\vec{L} = \vec{r} 	imes \vec{p} = \vec{r} 	imes (m\vec{v})$.For point $O$ (the center of the cir

Vedclass · Accepted Answer

$\vec{L}_O$ remains constant while $\vec{L}_P$ varies with time.

Vedclass · Answer

(C) The angular momentum about a point is given by $\vec{L} = \vec{r} 	imes \vec{p} = \vec{r} 	imes (m\vec{v})$.For point $O$ (the center of the circle),the position vector $\vec{r}$ is in the $x-y$ plane and the velocity $\vec{v}$ is tangential to the circle. The angular momentum $\vec{L}_O = \vec{r} 	imes m\vec{v}$ is directed along the $z$-axis (perpendicular to the plane of motion). Since the speed and radius are constant,the magnitude and direction of $\vec{L}_O$ remain constant.For point $P$ (a point on the $z$-axis),the position vector $\vec{r}'$ from $P$ to the mass $m$ changes direction as the mass moves in a circle. Consequently,the cross product $\vec{L}_P = \vec{r}' 	imes m\vec{v}$ changes its direction continuously as the mass rotates,even though its magnitude remains constant. Therefore,$\vec{L}_P$ varies with time.Thus,$\vec{L}_O$ remains constant while $\vec{L}_P$ varies with time.

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