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?