Add left arm like a piece of string not actively contributing to the stroke. Then left arm like a karate chop??? More confusion. Where is the right side in all this?? Homer is probably chuckling somewhere reading this thread.
It's the left shoulder that does the rope handling.
The arm is the rope.
Work = force * distance (Newton).
The shoulder pulls with a force.
And it moves in the direction it is pulling.
That means work. Work means producing energy.
The only energy we have here is moving mass. 1/2 Mass * velocity^2 to be precise. Newton once again.
The mass is constant. That leaves us with change of velocity.
Unless you do it really fast. When the swing speed approaches the speed of light we have to consult Einstein instead. Things get heavy then.