First slide

Angular momentum

Question

If a particle of mass m is moving with constant velocity v parallel to x-axis in x-y plane as shown in fig. Its angular momentum with respect to origin at any time t will be

Moderate

A

$mvb \hat{k}$
B

$- mvb \hat{k}$
C

mvb $\hat{i}$
D

mv $\hat{i}$

Solution

We know that, Angular momentum
$\dot{\vec{L}} = \vec{r} x \vec{P} in terms of component becomes$
As motion is in x-y plane (z = 0 and $P_{z} = 0), as \dot{\vec{L}} = \hat{k} ({xp}_{y} - {yp}_{x})$
Here x = vt, y = b, $p_{x} = mv and p_{y} = 0$
$∴$ $\vec{L} = \hat{k} [vt \times0- b mv] = - mvb \hat{k}$

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