Ok so say I have a shopping cart with the wheels that spin so it can easily move in any direction. I am pushing it along the x direction. You come along and push it from the side in the y direction. In now travels partly in the x and partly in the y direction. To find out the magnitude we take the product of x and y and obtain the square root. We now have a scalar magnitude of the force in the xy direction. What if we have one force in the positive x direction and another in the negative x direction as well as the one in the positive y direction? We now have stress components in 3 directions. And on it goes.So if I model these 3 or more forces as a tensor do I express each and all additional forces in terms of any convenient coordinate system?
What surprises me is that seemingly the final expression is the same when viewed from any other coordinate system , even one in motion wrt to it.
Any reason that should be so (I assume it is experimentally verified so long as I have understood this apparently simple scenario**)
** why does it always seem simple after and never before :-(