A particle of mass M moves with a constant ve | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The angular momentum $\vec{L}$ of a particle with respect to the origin is given by $\vec{L} = \vec{r} 	imes \vec{p}$,where $\vec{p} = M\vec{v}$.

Vedclass · Accepted Answer

Remains constant

Vedclass · Answer

(C) The angular momentum $\vec{L}$ of a particle with respect to the origin is given by $\vec{L} = \vec{r} 	imes \vec{p}$,where $\vec{p} = M\vec{v}$.Since the particle moves parallel to the $X$-axis with constant velocity $\vec{v} = v\hat{i}$,its position vector is $\vec{r} = x\hat{i} + y\hat{j}$.Thus,$\vec{L} = (x\hat{i} + y\hat{j}) 	imes (Mv\hat{i}) = Mv(x(\hat{i} 	imes \hat{i}) + y(\hat{j} 	imes \hat{i}))$.Since $\hat{i} 	imes \hat{i} = 0$ and $\hat{j} 	imes \hat{i} = -\hat{k}$,we get $\vec{L} = -Mvy\hat{k}$.Here,$M$,$v$,and $y$ (the perpendicular distance from the $X$-axis) are all constant.Therefore,the angular momentum $\vec{L}$ remains constant.

$A$ particle of mass $M$ moves with a constant velocity parallel to the $X$-axis. What happens to its angular momentum with respect to the origin?

Similar Questions

$A$ particle of mass $5 \ kg$ moves along the straight line $y = 2x + 4$ with a velocity of $3\sqrt{5} \ m/s$. Find its angular momentum about the origin in $kg \ m^2 \ s^{-1}$.

$A$ torque of $50 \ Nm$ acts on a body for $8 \ s$,which is initially at rest. The change in its angular momentum is:

$A$ particle of mass $1 \ kg$ is moving with a linear velocity of $2 \ ms^{-1}$ parallel to the positive $X$-axis. During this motion,its minimum distance from the origin is $12 \ cm$. The angular momentum of this particle about the origin is ....... $Js$.

$A$ mass tied to a string is whirled in a horizontal circular path with a constant angular velocity and its angular momentum is $L$. If the string is now halved,keeping the angular velocity the same,then the new angular momentum will be:

$A$ disc of mass $M$ and radius $R$ is rolling on a horizontal surface as shown in the figure. What is the magnitude of the angular momentum of the disc about the origin $O$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module