Do you really think that the same applies in baseball? That momentum is not important in baseball? That the mass of the bat is insignificant? I don't see much difference between golf and baseball when it comes to this discussion. The mass of a club is as important as the mass of a baseball bat. And they are both very important in the momentum equations that are needed when calculating ball speed
Dinosaur There is something about golf technique which may not understand. There are two kinds of swings; the low speed distance control swing [chip shot] and the high speed full swing [driver]. When a top player chips a ball from just off the green, he is primarily concerned with controlling the distance he hits it [direction for such a small swing is easy to control]. The phenomena he must avoid is the "kicking" of the shaft that will propel the ball much farther than he wants. In engineering terms, he wants to stay in the "linear region" where the force he applies is directly proportional to the distance he gets. If the shaft "kicks" [like say a fishing poll during a cast] then distance can not be predicted accurately. Golf buffs all know of the historic films that Bobby Jones took back in the 20's when there was great debate about what the shaft did at impact. The films clearly show the shaft kicks and the golf clubhead is actually AHEAD of the shaft axis line at impact. One times the swing so the head kicks in to the ball. For the chip shot there is a clear slow down in the head velocity and thus a momentum transfer much like with billiard balls. A nearly perfect elastic collision. http://en.wikipedia.org/wiki/Elastic_collision But for the drive, the clubhead speed does not seem to slow down thru impact and thus your thesis that there is no momentum transfer from the club to ball. That is how you conclude it is like a ball striking a wall. But the REAL impact is the kick of the shaft and the club does slow down considerably during this process thus yielding a collision with momentum transfer. It is a lot like a groundstroke in tennis. Films show the racquet clearly slowing down after impact. In golf it is just harder to see it.
Back to the OP's original question. What effect does the shaft have on MOI ? MOI is defined by Wikipedia as ..... a measure of an object's resistance to changes in its rotation rate. It is the rotational analog of mass. That is, it is the inertia of a rigid rotating body with respect to its rotation. The moment of inertia plays much the same role in rotational dynamics as mass does in basic dynamics So the OP wants to know the effect of the shaft on MOI. I will guess that it is proportional to the shaft's contribution to total club mass. Shafts typically are around 65 grams [Google "golf shaft weight"] Heads are around 190 grams Golf balls are 47 grams. I would think the total club mass determines MOI and so it should contribute proportionately. Thus it is nearly a 25% effect in terms of MOI. [ 65 / (65+190) ] But this is not accurate because the swing is NOT a pendulum swinging. It is more like a bullwhip cracking and thus the shaft's mass plays little part in the generation of initial velocity. It is the shaft stiffness that determines the frequency of vibration and thus the "kick speed" during impact. Gosh I must have too much time on my hands ! Back to inspiring Math students with well planned lessons and demonstrations.
Determining moment of inertia requires integration. If a point mass is distance r from the center of rotation, the MOI of that point mass is Mass*r[sup]2[/sup]. Think of a spinning ice skater: With arms & legs extended, the spin is much slower than with arms & legs close to center of rotation. PaulR's estimate is incorrect. A bit of mass 40 inches from the center of rotation would have 1600 times the MOI of a bit of mass one inch from the COR. It would have 4 times the MOI of a bit of mass 20 inches from COR. Since the shaft is not a uniform cylinder, calculating MOI is a bit painful. Since the head is farthest from the COI, the square law results in its contribution to the MOI being huge compared to the shaft's contribution. It would seem that the shaft's contribution to MOI is much less than the 25% suggested by PaulR. Given that the MOI of the shaft & head were calculated, what is the formula relating MOI to ball speed? I do not have a clue now & perhaps never did know such a formula. BTW: I do not think that ball speed has a linear relationship to club face speed at impact. I suspect that none of the variables have a linear relationship to ball speed. Hence, I do not think there is a simple answer to the questions posed in this thread. Again: The deformation & restoration of the shape of the golf ball has a significant effect on ball speed. That is the reason for golf balls having different compression characteristics. The touring pros use higher compression balls than duffers. There is a reason for this, although many duffers mistakenly use the same balls as the touring pros.
I am pretty sure that if you kept all other things constant (such as MOI), ball speed would be a nearly linear function of clubhead speed. I understand that it is a complicated equation trying to relate MOI to ball speed. I couldn't find it anywhere on the web and that's why I posted here.
John Connellan: Without some pertinent laws of physics, if the following is true, it is a lucky guess. Have you ever seen a high speed photograph of a golf ball or baseball during impact? If you had, you would not be so quick to ignore the effect of ball deformation & recovery to the original shape. I think that the higher the club head velocity, the more the deformation & the longer the ball stays in contact with the club face. Since a pro golfer is applying torque force to the ball via the shaft while the ball is in contact with the club face, extra contact time should have an effect on ball speed. I expect club head speed to affect both the amount of deformation & the time that the ball is in contact with the club face. My intuition suggests that ball speed is not a linear function of club head speed. My intuition has been wrong in the past, so I would not bet much money on it.
That's why I said nearly linear. I know there are a few very small variables such as deformation etc. However, the increase in ball speed would not be significant IMO. Perhaps 1 or 2 mph more from a slow swing speed to a fast one. What is even more difficult for me to visualise is how ball speed might relate to moment of inertia keeping everything else constant.
