I got several questions this last time around, and I don't remember for sure who asked what, so I'll just try to cover it in general, and hit the "high spots". Inertia is a minifestation, a property, an effect, of acceleration and deceleration. It's proportional to the square of the change in speed, or velocity. Acceleration and deceleration are changes in velocity. The velocity, or speed, of a mass revolving about a central point is proportional to the radius of the orbit of that mass. Therefore, the moment of inertia is proportional to the square of the radius, or the square of the acceleration or decelaration. If you are slinging a rock in a sling at the rate of two RPS, its force on the sling will be four times what it would be at one RPS. In the case of the rock in the sling, we are dealing with centripetal acceleration. These are just different manifestations of the same thing. Inertia is simply the resistance a mass has to being accelerated or decelarated, or forced to change direction. You will find this discussed in a variety of textbooks. If we release the rock from the sling, and measure how hard it hits, we will find that it hits four times as hard when it is traveling twice as fast. This is kinetic energy. Kinetic energy and inertia are first cousins. Inertia, as Don reminded us, is an effect, or property, and kinetic energy is a measurable quantity. If we are looking at one complete key system, from key front to hammer head, we are, in effect, just looking at a compound lever. The acceleration and decelaration of the hammer head dominates the action inertia, because that's where the velocity changes the most, and as we said, that effect is not linear. It's a square function. If we just look at the key all by itself, we will be kidding ourselves. As for the effect the pianist feels on the key, the static weight is simply multiplied by the total action ratio. But since the moment of inertia varies as the square of the radius, or the lever arm, the moment of inertia of the hammer head must be its mass multiplied by the square of the total action ratio to determine what its inertia will feel like to the pianist. This still neglects the moments of inertia of the other action components. I'm not sure exactly how I will do the experiment, but I have some ideas. I'll have to see what gives me some measurable, definitive results. No, I don't have a suitable high-speed camera, but I can rig up some sensors that can "look" at the hammer and the key, and that will tell me when something starts to move, how fast it accelerates, and when it reaches a certain position. I can display the signals on a scope, or with a computer, and time it to a fraction of a millisecond. I won't post it unless I can come up with something that's meaningful, but I believe I can. What I want to see is how long it takes the jack to get back under the knuckle, under the following conditions: 1. Key weighted in the usual way, 2. Key weighted near the center, 3. Key with no lead, but very strong wippen assist spring. Same key, same action parts, in each case. It will probably be sometime in January 2004 before I'll have anything to report. Merry Christmas, Jim Ellis
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