If force vec{F} = 3 hat{i} + 4 hat{j} - 2 hat | vedclass

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

Question

(B) The torque $\vec{	au}$ is given by the cross product of the position vector $\vec{r}$ and the force vector $\vec{F}$:$\vec{	au} = \vec{r} 	imes

Vedclass · Accepted Answer

$-10 \hat{i} + 10 \hat{j} + 5 \hat{k}$

Vedclass · Answer

(B) The torque $\vec{	au}$ is given by the cross product of the position vector $\vec{r}$ and the force vector $\vec{F}$:$\vec{	au} = \vec{r} 	imes \vec{F}$Using the determinant form for the cross product:$\vec{	au} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 2 & 1 & 2 \ 3 & 4 & -2 \end{vmatrix}$Expanding the determinant:$\vec{	au} = \hat{i} [(1)(-2) - (2)(4)] - \hat{j} [(2)(-2) - (2)(3)] + \hat{k} [(2)(4) - (1)(3)]$$\vec{	au} = \hat{i} [-2 - 8] - \hat{j} [-4 - 6] + \hat{k} [8 - 3]$$\vec{	au} = -10 \hat{i} + 10 \hat{j} + 5 \hat{k}$

If force $\vec{F} = 3 \hat{i} + 4 \hat{j} - 2 \hat{k}$ acts on a particle having position vector $\vec{r} = 2 \hat{i} + \hat{j} + 2 \hat{k}$,then the torque about the origin will be:

Similar Questions

Let a force $\vec{F} = -F\hat{k}$ act on the origin of a Cartesian frame of reference. The moment of force about a point $(1, -1)$ will be

Which type of motion exists due to the moment of force (couple)?

$A$ door is hinged at one end and is free to rotate about a vertical axis (figure). Does its weight cause any torque about this axis? Give a reason for your answer.

If $\vec{F} = (5 \hat{i} - 10 \hat{j}) \text{ N}$ and $\vec{r} = (4 \hat{i} - 3 \hat{j}) \text{ m}$,then the torque $\vec{\tau}$ acting on the object will be:

Which forces are needed for the rotational motion about a fixed axis?

Vedclass Test Series

Exam Paper Generator

Online Exam Module