First slide

Rotational motion

Question

A particle of mass m moves in the XY-plane with a constant velocity ‘V’ along the straight line $X' Y'$ . If the angular momentum of the particle with respect to origin O is $L_{A}$ when it is at A, and $L_{B}$ when it is at B, then

Moderate

A

$L_{A} > L_{B}$
B

$L_{A} = L_{B}$
C

The relationship between $L_{A} and L_{B}$ depends upon the slope of the line AB
D

$L_{A} < L_{B}$

Solution

Since the particle is moving on a straight line with a constant speed, the velocity will remain constant
As we know $\vec{L} = \vec{r} \times m \vec{v}$
$\Rightarrow |\vec{L}| = m v r$
r= Perpendicular distance
v= Speed
m= Mass
We can see at point A and B the product mvr is constant.
Hence $|{\vec{L}}_{A}| = |{\vec{L}}_{B}|$
$\Rightarrow L_{A} = L_{B}$
Therefore, the correct answer is (B).

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