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

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

Question

(D) The angular momentum $\vec{L}$ of a particle about a point $O$ is given by the cross product of its position vector $\vec{r}$ and its linear momen

Vedclass · Accepted Answer

$mv\ell$

Vedclass · Answer

(D) The angular momentum $\vec{L}$ of a particle about a point $O$ is given by the cross product of its position vector $\vec{r}$ and its linear momentum $\vec{p} = m\vec{v}$.Mathematically,$\vec{L} = \vec{r} 	imes \vec{p} = \vec{r} 	imes (m\vec{v}) = m(\vec{r} 	imes \vec{v})$.The magnitude of the angular momentum is given by $L = mrv \sin(	heta)$,where $	heta$ is the angle between the position vector $\vec{r}$ and the velocity vector $\vec{v}$.From the geometry of the figure,the perpendicular distance from the origin $O$ to the line of motion $PC$ is $\ell$.Therefore,the magnitude of the angular momentum about $O$ is $L = m v \ell$.

$A$ particle of mass $m$ moves with a velocity $v$ along the line $PC$ as shown in the figure. What is the angular momentum of the particle about $O$?

Similar Questions

The time dependence of the position of a particle of mass $m = 2 \ kg$ is given by $\vec r(t) = 2t \hat i - 3t^2 \hat j$. Its angular momentum with respect to the origin at time $t = 2 \ s$ is:

$A$ particle of mass $m = 5$ is moving with a uniform speed $v = 3\sqrt{2}$ in the $XOY$ plane along the line $Y = X + 4$. The magnitude of the angular momentum of the particle about the origin is .......

Angular momentum is

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

The angular momentum of a body is the product of which of the following?

Vedclass Test Series

Exam Paper Generator

Online Exam Module