Here's why:
* Angular momentum is a vector quantity. It has both magnitude and direction. The direction is perpendicular to the plane formed by the position vector and the linear momentum vector.
* Linear momentum is also a vector. It's the product of mass and velocity.
* The key is the angle between the position vector and the linear momentum vector. If the particle is moving directly towards or away from the origin (i.e., its velocity is parallel to the position vector), then the angle between them is 0 or 180 degrees. In this case, the angular momentum is zero because the sine of 0 or 180 degrees is zero.
However:
* If the particle's motion is not directly towards or away from the origin, there is a non-zero angle between the position vector and the linear momentum vector. This leads to a non-zero angular momentum.
Example:
Imagine a particle moving in a straight line that passes through the origin, but the line is not perfectly horizontal or vertical. The particle's velocity has both horizontal and vertical components. This means there's an angle between its position vector and its velocity vector, resulting in non-zero angular momentum.
In conclusion:
While a particle moving along a line passing through the origin could have zero angular momentum if it's moving directly towards or away from the origin, it's not guaranteed. The angular momentum depends on the angle between the particle's position vector and its linear momentum vector.
