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Moment of Inertia
For those interested in more details of the concept of moment of inertia, you can think of a ball attached to the end of a string, being whirled about in a circle. Or a flywheel, which is conceptually the same. The longer the string, or the longer the radius of the flywheel, the more difficult it is to accelerate the ball or the flywheel rim. Likewise if you make the ball, or rim of the flywheel, heavier ( more mass technically speaking ) the more difficult it is to accelerate.
The opposite is also true. If the length, or the weight, or both, can be reduced the easier it is to accelerate and rotate the outside object. Two things are critical – mass, and how far is it from the axis of rotation.
The general algebraic formula is,
MOI = mass times length squared, or I = ML2 . Different shape configurations produce different specific MOI’s. In the case of our weight on the end of a string MOI would be, I = ML2/1. An electric motor can be considered a solid cylinder rotating on an axis which happens to be its shaft. The motor’s MOI therefore is, I = MR2/2. Our flywheel has a rim rotating about its axis, like the motor. Its MOI = MR2/1. A uniform stick, say a dowel, when rotated about its end, has an MOI = ML2/3. The same dowel, when twirled in its middle like a baton, has a much lower value of, MOI= ML2/12. It quickly becomes obvious that the interaction of length squared times mass yields greatly varying results.. How far each particular mass is from the axis of rotation determines the outcome. In trying to reduce MOI it becomes clear that bringing the total mass closer to the axis, even by a small amount, lowers it a lot. This is because length is a factor that is squared as you multiply. These examples are all regular shaped objects, pretty easy to handle. However, a golf club is an irregular shaped object with a lot of mass at its end, which makes it a more difficult problem.
Because of its shape, and relatively heavy head weighting, the center of mass of a golf club is not on the club itself but is located somewhere off the shaft and above the club head. The axis of rotation is where the two hands meet as one grips the club, approximately 5 inches down from the butt end. To properly calculate MOI each little segment of mass must be isolated and multiplied by its distance squared back to the 5 inch axis point of the grip. Then all those many discreet values are added up for the final value. This would be cumbersome to do in practice but for those experienced in integral calculus, it is relatively easy to calculate.
Proper MOI’s must be different for various skill levels, and anatomies. One size will not fit all. For example a strong, muscular player who is a long hitter will tend to want a high MOI. He can swing that club just as fast as a low MOI club without undue exertion. It allows him or her to feel the club head better during the swing – to know where it is when going back and when coming down. He needs it for timing and for square hits.
Other players have different needs. A short player may have the strength to swing a long club but have problems because the length produces an excessively flat swing, causing open face contact with the ball. In which case the best solution is to make the clubs shorter and use slightly heavier heads. Or a tall player may need longer clubs but doesn’t quite have the strength to swing them. The only practical solution is to lower the MOI by some combination of complex tricks. As mentioned previously, our proprietary values have been established over the years, observing players of every caliber.
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