IIT JEE , AIEEE Forum - Physics , Mechanics

srujana

Please let me know the differences between polar and axial vectors

striker

There are two types of vectors in use 3D geometry and physics: Displacement (or Polar) and Axial. Polar vectors are typically used to refer to the location of things, or the displacement between two points, or the direction of velocities/forces/etc. Axial vectors are typically used in relation to rotation, and typically refer to the direction of the axis of rotation.

The major difference between axial and polar vectors is how they transform with an inverting transformation (i.e. a transformation which converts from a right-handed coordinate system to a left-handed one or vice versa). Polar vectors are inverted with such transforms, axial vectors aren't.

As an example, take an object which at time t=0 is at location r0=(1,0,0) and has a velocity v=(0,1,0). Its position at any future time is r(t) = (1,t,0) and it has a angular momentum of ? = rXv = (0,0,1). Under the coordinate transformation x'=-x, y' = -y, z'=-z, the radial vectors r'0, r'(t), and v' become (-1,0,0), (-1,-t,0), and (0,-1,0) respectively, which physically refers to the same conditions. However, r'Xv' = (0,0,1), which is not what you get by transforming ? (?' = (0,0,-1)).

Because axial and polar vectors do not transform the same way, it is generally considered a bad idea to add axial and polar vectors together.

THIS IS NOT MY IDEA
I TOO DON'T KNOW ABT THIS NOW BCOZ OF UR POST I DO KNOW THEM
HOWEVER THANKS MISS
CHEERSSSS

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