First slide

Angular momentum

Question

The position of a particle is given by $\vec{r} = (\hat{i} + 2 \hat{j} - \hat{k})$ , linear momentum by $\vec{P} = (3 \hat{i} + 4 \hat{j} - 2 \hat{k}) .$ The angular momentum is perpendicular to

Moderate

A

x-axis
B

y-axis
C

z-axis
D

Line at equal angles to all the three axes

Solution

$\vec{L} = \vec{r} \times \hat{p} = (\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & 2 & - 1 \\ 3 & 4 & - 2 \end{matrix}) = - \hat{j} - 2 \hat{k}$
i.e., the angular momentum is perpendicular to x-axis.

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