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- Thread starter undereducated
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As you know, when an object is spinning around an axis, it can spin either clockwise or counterclockwise. Assuming an object is located at the origin, the angular momentum vector will happen to be along the axis it is spinning around. Furthermore, whether the vector is pointing up or down (relative to the position and linear momentum vectors) tells you whether it is spinning clockwise or counterclockwise. The magnitude of the vector tells you how much angular momentum it has.

One reason that we do this instead of pointing the vector in the direction the object is spinning is that if you have a vector pointing in the direction it is spinning, how do you know where to "attach" the vector to the object to determine the direction it is spinning? You might say that we can just attach it to the r we used. But then, the direction of the vector would only make sense for one given r, when the actual formulation makes sense for all given r.

If you need anything elaborated on, just say so.

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Vector math is easier, so vectors are used to deal with angular momentum, torque, acceleration, ... The vector coincides with the axis of rotation, and the length of the vector represents a magnitude.

Angular position is a bit tricky, since it's just an angle, and you'd need some consistent rule for what a position of zero angle is.

Regarding cross product, it just works out that the cross product of a linear radial vector and a linear tangental vector produces an appropriate vector to represent an angular quantity, such as torque = radius times force.

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Consider the alternative of using a two dimensional "disc" to represent angular components. The size of the disc could represent the magnitude, and the axis of the disc would be the axis of rotation of the object being represented. The problem is how to perform math on planes instead of vectors.

That's interesting! I think area is also a cross product - do you think that's a way to go from your disc idea to the cross product?

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i.e for like a spinning top,

i don't get why, i would've thought it was along the x-axis due to some kind of PI product?

L=IW

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It's actually located in the X-Y plane but as I mentioned above, how do you do math with "planes" or "discs" as opposed to vectors? It's just a convention to mathematically represent angular momentum as a vector perpendicular to the plane of rotation.why does the angular momentum go through the z axis?

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I know there are two right hand rules. Some people use the one where three fingers stick out. I'm talking about the one in this picture: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html.

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It doesn't, left hand rule would work just as good. In the cases of charged particle centripetal acceleration perpendicular to fields, we chose a sign for the direction of the fields and particles that work with right hand rule. We also chose to mathematically represent current flow in the opposite direction of electron flow, something that could be changed but isn't because we can't teach the old mathematicians and physicists new tricks.Why does the right hand rule apply in nature?

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