Physics - Rotation Question with Solution | TestHub

The relation between linear velocity $\vec{v}$, angular velocity $\vec{\omega }$, and radius vector $\vec{r}$ is given by $\vec{v}=\vec{\omega }\times \vec{r}$.

Substituting the given vectors:

$\vec{v}=(3\hat{i}-4\hat{j}+\hat{k})\times (5\hat{i}-6\hat{j}+6\hat{k})$

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

$\vec{v}=\hat{i}[(-4)(6)-(1)(-6)]-\hat{j}[(3)(6)-(1)(5)]+\hat{k}[(3)(-6)-(-4)(5)]$

$\vec{v}=\hat{i}(-24+6)-\hat{j}(18-5)+\hat{k}(-18+20)$

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

Answer: $(-18\hat{\mathrm{i}}-13\hat{\mathrm{j}}+2\hat{\mathrm{k}})$