For a particle,the angular velocity is vec{om | vedclass

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

Question

(A) The linear velocity $\vec{v}$ is given by the cross product of angular velocity $\vec{\omega}$ and position vector $\vec{r}$:$\vec{v} = \vec{\omeg

Vedclass · Accepted Answer

$-5\hat{i} + 2\hat{j} + 3\hat{k}$

Vedclass · Answer

(A) The linear velocity $\vec{v}$ is given by the cross product of angular velocity $\vec{\omega}$ and position vector $\vec{r}$:$\vec{v} = \vec{\omega} 	imes \vec{r}$$\vec{v} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 1 & -2 & 3 \ 1 & 1 & 1 \end{vmatrix}$Expanding the determinant:$\vec{v} = \hat{i}((-2)(1) - (3)(1)) - \hat{j}((1)(1) - (3)(1)) + \hat{k}((1)(1) - (-2)(1))$$\vec{v} = \hat{i}(-2 - 3) - \hat{j}(1 - 3) + \hat{k}(1 + 2)$$\vec{v} = -5\hat{i} - \hat{j}(-2) + 3\hat{k}$$\vec{v} = -5\hat{i} + 2\hat{j} + 3\hat{k}$

For a particle,the angular velocity is $\vec{\omega} = \hat{i} - 2\hat{j} + 3\hat{k}$ and the position vector is $\vec{r} = \hat{i} + \hat{j} + \hat{k}$. What is the linear velocity $\vec{v}$?

Similar Questions

Regarding the rotation of the Earth about its axis:

$A$ uniform solid cylinder of mass $M$ and radius $R$ rotates about a frictionless horizontal axle. Two similar masses $m$ are suspended with the help of two ropes wrapped around the cylinder. If the system is released from rest,then the acceleration of each mass will be

What are the characteristics of rotational motion?

Obtain the relation between linear velocity and angular velocity of rotational motion of a body.

Vedclass Test Series

Exam Paper Generator

Online Exam Module