I was told that the sum of linear and angular momentum is conserved.
Given that angular momentum's direction as a vector is completely arbitrary (I believe there is no physical reason for choosing the cross product going the way it does (that is, perpendicular up or down, it just matters that it's perpendicular), correct me if I'm wrong), and linear momentum is often interchanged into angular momentum, surely the vector sum cannot be conserved?
Or am I wrong, and the meaning is that the magnitude is conserved?
As a sidenote, I suppose this would be a good place to ask why such an odd system was devised for calculating the direction (not magnitude) of angular momentum. Why not have the arrow pointing in the direction of motion, with its base at the point that we are considering angular momentum about? Is it useful simply to compute the conservation of it about a point, as it just involves addition?