First of all, Thank you Jeff for asking some very interesting questions regarding TGM - in this thread as well as in others.
And even though the endless belt analogy has some merits, I certainly agree that concepts that are close to the real thing are better than those who are farther away.
But angular acceleration isn't what this is about. Angular acceleration is often regarded as one of the most differentiating factors between swinging and hitting, and is possible one of the most misunderstood concepts in golf.
Angular acceleration does not increase the speed of whatever is being rotated. Angular acceleration doesn't do anything but change the direction while conserving energy. It is only longitudinal force that can increase the club spead. Or shoud I say: "Geometrically Orienteted Linear Force" - G.O.L.F
In a pure swing, the swing center is shifting. It is always moving a little ahead of the rotation center. Rotation of left shoulder joint is key here. I personally believe that the role, position and movement of the left shoulder joint is underestimated in TGM as far as swinginging is conserned.
This shifting of center is creating a longitudinal force component in addition to the centripetal force component of the "pulling string". The pulling string is used to pull & rotate at the same time. The longitudinal force component is what increases speed. The centripetal force component only takes care of the circular part and doesn't produce speed.
Think of David Leadbetters illustration when he spins a little something attached to a tiny rope. He has to move his hand in a circle to pick up speed.
Only longitudinal force produces work. And work is required to increase the speed. It is the longitudinal force of the swing that increases the clubhead speed. Or should I say: Geometrically Oriented Linear Force: G.O.L.F.
And Newton has explained why there is no other way.
It is possible to do a pure swing and a pure hit from the same top position, and have the same club alignment at impact and basically the same speed too. These facts are strong indications that the two stroking methods basically containes the same amounts of angular acceleration (the part that caused the rotation) and longitudinal acceleration (the part that increases the speed). One of them would miss the ball othervise.
I don't think the water skiing analogy works without water drag. It is the water drag that enables the skier to go in another direction than the boat, and this is a sort of overtaking action. As long as the skier is coming up from behind he will have larger speed than the boat - even relative to the course the boat is going. But the skier will have largest speed when he goes in the direction that is most different to the boat - when he comes back from a far left, is straight behind the boat and aiming far right. The true analogy to golf here is, I believe an overtaking action. A transfer of energy from boat to skier. A skilled and heavy skier will significantly slow down the boat. Some of the energy will be wasted to water shuffling, but some of it will accelerate him to the right.
If the boat went in circles, and managed to keep with up the skier, he could be straight behind the boat aiming far right and picking up speed all day long.
Looking at the Bobby Jones sequence, the swing seems to have a very steady linear force as the club is acellerating gradually.
Looking at Tiger's swing, something interesting seems to be happening around 9 o'clock in the downswing. Is the clubhead slowing down for a brief moment? Is he manipulating the geometry in order to increase the G.O.L.F from that point and through the ball?
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