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I don't understand why the angular momentum remains constant even after the distance of the particle (from the origin) keeps on increasing.

Maybe I'm not reading the graph the way it is but I don't understand why it remains constant.

If you could, please, explain.

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$$\vec L=m\vec r \times \vec v$$

$$L=mvrsin(\theta)$$

The formula gives you the answer if you think about it. You could think of the vectors $\vec r$ and $\vec v$ in the following way:

The particle moves from A to B on a straight line. However you draw a position vector $\vec r$ to the point on the line from the origion $O$, all you are really interested is in the component of the position vector perpendicular to the velocity vector.

Here, the velocity vector $\vec v$ points along the same direction throughout its journey (along the line). If you draw a right angled triangle over the line :

enter image description here

In $\triangle OPC$, you can see that $OP$ is the side $rsin(\theta)$. And from that $\vec L$ turns out to be constant in both direction and magnitude.

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