As you might suspect, when you reverse the current in an alternating current motor, it takes time for those atoms to get going in the opposite direction. And the amount of time is not necessarily the same as the time it took to get the herd moving properly in the first place.
Magnetically soft materials, however, tend to be more expensive. The motor manufacturer must find that proper blend of just enough magnetically soft material to do the work required without putting too big a dent in the customer wallet.
For wiring a single-phase motor, the most important objective is to distinguish the starting circuit from the main winding. These two circuits are isolated from one another electrically if the lead wires are separarted and not in contact with each other. Initially, the ohmeter can be used to determine which wire belongs to which circuit as well as checking continuity between leads.
If you are confused by me saying that the current flows from positive to negative, that just happens to be a historical convention. People like Benjamin Franklin, who helped figure out the mystery of electricity back in the 18th century, believed it was a flow of positive charges, so it flowed from positive to negative. We call this idea conventional current and still use it to this day in things like Fleming Left-Hand Rule.