First slide

Angular momentum

Question

A particle of mass 2 kg located at the position $(\hat{i} + \hat{j}) m$ has a velocity $2 (+ \hat{i} - \hat{j} + \hat{k}) {ms}^{- 1}$ Its angular momentum about Z-axis $(in kg - m^{2} s^{- 1})$ is

Moderate

A

+4
B

+8
C

$-$ 4
D

$-$ 8

Solution

About origin, angular momentum will be
$L = m (r \times v) = 2 |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & 1 & 0 \\ 2 & - 2 & 2 \end{matrix}| = 4 \hat{i} - 4 \hat{j} - 8 \hat{k}$
Therefore, component of angular momentum about Z-axis would be $- 8 kg \cdot m^{2} s^{- 1}$ .

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