[Paddlewise] Why does rocker and carving work?

I'm trying to understand why rocker makes a boat turn
easier.  My current idea is that if a boat drafts 6
inches all the way along, a sweep stroke or other
force such as a wave has 6 inches to work against at
the end of the boat.  However, if there is rocker, the
power of the sweep stroke is pushing against only a
couple of inches and it takes less force to move the
bow on a pivot point back near the paddler.  Is this
correct?

Also, when a kayak is leaned with the right knee, does
the boat turn because the water on the right side has
a longer path and thus the left side is able to move
quicker through the water so that the boat ends up
turning to the right?  

Scot

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