First slide

Angular momentum

Question

A particle of mass m moves with a constant velocity. Which of the following statements is not correct about its angular momentum about origin?

Moderate

A

It is zero when it is at A and moving along OA.
B

It is same at all points along the line DE
C

It is of the same magnitude but oppositely directed at B and D.
D

D It increases as it moves along the line BC.

Solution

Angular momentum of a particle about a point can be given by the cross product of its position vector and the momentum vector.
$| \vec{L} | = | \vec{r} \times \vec{p} | = mvrsin (θ)$
$= {mv}_{⊥} r = {mvr}_{⊥}$
$\hat{L} = \hat{r} \times \hat{p}$
It simplifies to the product of distance and the tangential velocity. The direction can be given by the right hand thumb rule.
As the particle moves along OA, the position vector and momentum vector are colinear so the cross product is zero.
Along DE the cross product of the momentum vector and position vector always points towards out of the plane of paper.
Along BC the cross product of the momentum vector and position vector always points into the plane of paper.
Along BC and DE the magnitude of the cross product is the same.

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