Question

What is the value of linear velocity if $\omega =3\hat{i}-4\hat{j}+\hat{k}$ and $r=5\hat{i}-6\hat{j}+6\hat{k}?$

• A. $6\hat{i}+2\hat{j}-3\hat{k}$
• B. $-18\hat{i}-13\hat{j}+2\hat{k}$
• C. $4\hat{i}-13\hat{j}+6\hat{k}$
• D. $6\hat{i}-2\hat{j}+8\hat{k}$

Answer 1

The correct option is B $-18\hat{i}-13\hat{j}+2\hat{k}$

The relation between linear velocity and angular velocity is

$\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r}$

$\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& -4& 1\\ 5& -6& 6\end{array}\right|$

$\overrightarrow{v}=-18\hat{i}-13\hat{j}+2\hat{k}$