Physics - Rotation Question with Solution | TestHub

The angular momentum $\vec{L}$ of a body is given by the cross product of its position vector $\vec{r}$ and linear momentum $\vec{p}$.

$\vec{L}=\vec{r}\times \vec{p}$

Substituting the given vectors:

$\vec{L}=(2\hat{i}+3\hat{j}-3\hat{k})\times (2\hat{i}+4\hat{j}-5\hat{k})$

$\vec{L}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& 3& -3\\ 2& 4& -5\end{array}\right|$

Expanding the determinant:

$\vec{L}=\hat{i}[3(-5)-(-3)(4)]-\hat{j}[2(-5)-(-3)(2)]+\hat{k}[2(4)-3(2)]$

$\vec{L}=\hat{i}(-15+12)-\hat{j}(-10+6)+\hat{k}(8-6)$

$\vec{L}=-3\hat{i}+4\hat{j}+2\hat{k}$

Answer: $-3\hat{i}+4\hat{j}+2\hat{k}$