First slide

Angular momentum

Question

A particle of mass 2kg, located at position $(\hat{i} + \hat{j})$ units has velocity $2 (\hat{i} - \hat{j} - 2 \hat{k})$ units. Its angular momentum about origin is

Moderate

A

Zero
B

8 $\hat{k}$
C

12 $\hat{k}$
D

$4 (- 2 \hat{i} + 2 \hat{j} - 2 \hat{k})$

Solution

$\vec{L_{0}} = \vec{r} x \vec{mv} = (\hat{i} + \hat{j}) x 2 x 2 (\hat{i} - \hat{j} - 2 \hat{k}) units$
$\Rightarrow \vec{L_{0}} = 4 |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & 1 & 0 \\ 1 & - 1 & - 2 \end{matrix}| = 4 (- 2 \hat{i} + 2 \hat{j} - 2 \hat{k}) units .$

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