Question

The angular velocity of a rotating body is $\overrightarrow{\omega }=4\hat{i}+\hat{j}-2\hat{k}$. The linear velocity of the body whose position vector is 2$\hat{i}+3\hat{j}-3\hat{k}$ is:

• A. $5\hat{i}+8\hat{j}+14\hat{k}$
• B. $3\hat{i}+8\hat{j}+10\hat{k}$
• C. $8\hat{i}-3\hat{j}+2\hat{k}$
• D. $-8\hat{i}+3\hat{j}+2\hat{k}$

Answer 1

The correct option is B $3\hat{i}+8\hat{j}+10\hat{k}$

Linear velocity is given by the cross product of angular velocity and position vector.
$\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r}$
$\overrightarrow{v}=(4\hat{i}+\hat{j}-2\hat{k})\times (2\hat{i}+3\hat{j}-3\hat{k})$
$=(-3+6)\hat{i}+(12-4)\hat{j}+(12-2)\hat{k}$
$=3\hat{i}+8\hat{j}+10\hat{k}$