Cause vs Effect
 

Force is cause. Applying force results in movement. Angular momentum is effect. Mass moving about a fixed point has angular momentum. Applying force (cause) results in the club acquiring angular momentum (effect).

Closely related family members "getting together" (cause) results in (somewhere along the family tree or evolutionary tree - your pick) Bucket (effect). ;-) See you already understood the concept, but just had not applied it to the physics (wasn't this easy)!:p

Merry-Go-Round -- Push or Pull
 

Very nice, Steph. That concise explanation helps us all.

Bucket, with Steph's description in mind, think of pushing a playground merry-go-round into its rotating motion. The straight line thrust (force) causes the merry-go-round (the mass rotating about a fixed point) to acquire its rotating motion (and hence its angular momentum).

The straight-line 'push' is against the centripetal force of the merry-go-round's fixed structure, and as a G.O.L.F. analogy, is a Hitting Motion.

Similarly, the identical angular momentum could be created by turning the axis of the merry-go-round, thereby inducing a centrifugal force and its 'pull'. This is analagous to the Swinging Motion.

The far end speeds up when the radius gets shortened, and vice versa, which could be manipulated to regulate the clubhead speed.

I'm, however, not aware of COAM for clubhead manipulation, I strictly manipulate "lag" (or "club weight" or "shaft bent/stress") in swinging, hitting or snapping.

Apology
 

Bucket,

I want to apologize. I completely missed the "angular" in your question. I was so concentrated on conservation and momentum, that I answered the wrong question. I literally went off on a tangent. :laughing9

Angular momentum is a bit difficult to get a handle on in the golf stroke because you have 3-dimensional motion of an assembly that can be roughly approximated by a double pendulum. Here are some references which you might find interesting: http://hyperphysics.phy-astr.gsu.edu/hbase/amom.html, http://scienceworld.wolfram.com/phys...ePendulum.html.

I like this example - it shows why tempo - transition, and gravity are important - the ratio of back to through in time.

Chaos
 

The double pendulum is an example of a "simple" system whose motion results in chaotic behavior. Thus, the similarity of the golf stroke is not surprising.

Looks like my stroke of late:(

Ah, but this can lift some fog for any true swinger IMO

The image shows you why there have been many who speak of 'complete the backswing' or 'pause at the top' or 'wait for it' as transition swing keys.

The image shows you what happens if you start down too quick/too soon - throwaway ;)

There are also some lessons here for the aiming point concept.....and loading

One of the reasons I love the Tour Tempo sounds - they show you how to make sure you don't start down too soon - how to let gravity help you with your timing so that 'lower pendulumn' doesn't out race the upper and throw the club away.


I suspect many may dismiss this as a minor point - but if you are a swinger, a very, very important image to understand (why this shows a bad example, and what a 'true swing' would need to be for there not to be throw away)

Steph - do you know the calculation which would show what the ratio of back to through would need to be (in time) of the primary pendulumn for the secondary pendulumn not to have throw away (until about 7-8 o'clock as 'in line')? Just curious if my understanding of a 3 to 1 ratio (pi) is correct.

Experimentally Derived
 

Ed,

I think the Tour Tempo 3 to 1 factor was experimentally or observationally derived. It would not be easy to solve the double pendulum equations to arrive at that ratio. Basically, that double pendulum figure is being driven strictly by gravity. There are no other forcing functions. In the golf stroke with forces active during takeaway and the down swing, it gets very complicated to derive timing ratios like you are looking for. Someone may have done it, but I am not aware of such work. Sorry.

COAM is not something you CAN manipulate.
COAM is what happens on the way to the ball
Conservation of Energy is what happens at the ball


Part 1. Angular momentum is about what happens on the way to the ball. Whether you hit, swing, push or pull, angular momentum is going to be conserved regardless of what you do. However, the more you can sustain the lag, the more momentum has to be generated on the other side of the equation (i.e. transferred into the ball) for momentum to be conserved. What happens is that you start out with a large center of rotation (big wheel) of the club generally around your left shoulder. As you rotate down the plane and sustain the lag, you are shifting the primary center of rotation of the club to a point in your hands (small wheel), The longer you sustain the lag, the smaller the small wheel, and like the ice skater pulling in her arms, the faster the clubhead mass must travel to conserve angular momentum. Thus, the clubhead arrives at impact with an amount of kinetic energy, which like momentum is conserved.

Part 2. If you think about the impact interval being only a fraction of an inch or so, you can essentially consider this segment of the swing arc as a straight line, and thus, the collision between the ball and the clubhead is about the conservation of energy. The clubhead developed a certain amount of kinetic energy (1/2 m*v^2) during the pre impact interval, and some of that is going to be transferred to the ball through the collision. As Steph mentioned, the collision is elastic and there are some small losses associated with deforming the ball, and the clubface, but these are small. The efficiency of the energy transfer between the clubhead and the ball is related to the purity of contact, meaning mostly contact along the line of compression/direction of flight. Energy is lost to creating spin. Much of the energy is transferred to the ball. So, the simple balance is: (1/2 m1*v1^2 - losses)(clubhead) = 1/2 m2*v2^2.(ball)*

So what this is all about is creating the maximum kinetic energy just prior to impact. Sustaining the lag as long as possible creates the smallest center of rotation, and thus the maximum velocity since the clubhead mass didn't change. Hit, swing, push, pull, these principles don't change.

*Note: this is not rigorously correct since the impact interval is a slight arc, and not a precisely straight line. However it is pretty close.

G2M