## Zero Angular Momentum

Hello,

I am currently reading about angular momentum. A sentence in my textbook sort of confused me: "when the translational velocity of the particle is along a line that passes through the axis, the particle has zero angular momentum with respect to the axis."

I was wondering if someone could explain what the author is trying to convey.
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 Are they basically saying that the linear momentum of the particle is parallel to the perpendicular distance between the particle and axis of rotation? When would a situation like that ever occur? That seems kind of strange.
 Recognitions: Science Advisor They are saying that a particle moving in radial direction has no angular momentum. Which is entirely correct.

## Zero Angular Momentum

It sounds like he is talking about angular momentum (of a particle), which is a little different. A Google search for "momentum of a particle" will find plenty of info.

The angular momentum of a particle with respect to some point, is the cross product of the position vector of that particle with the vector of its (linear) momentum. In the case you mention, zero translational velocity in a particular direction of course means zero translation momentum in that direction, and therefore the cross product which gives the angular momentum will be zero.

 Quote by Bashyboy Hello, I am currently reading about angular momentum. A sentence in my textbook sort of confused me: "when the translational velocity of the particle is along a line that passes through the axis, the particle has zero angular momentum with respect to the axis." I was wondering if someone could explain what the author is trying to convey.
The particle has zero angular momentum with respect to any point on the axis.

The angular momentum of a particle with respect to a point is the cross product of the displacement vector from the point to the particle, and the linear momentum of the particle with respect to that point. If the displacement vector is parallel to the linear momentum, the cross product of the two vectors is a zero vector.

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