From: Randall Peters PETERS_RD@..........

Date: Sun, 17 Feb 2008 14:04:41 -0500

Barry, I'm not sure what it is you're trying to say about accelerometers. Just like any other `seismic' instrument, what they DIRECTLY respond to is ACCELERATION, not displacement. For frequencies of excitation less than the natural frequency of the accelerometer, the displacement can be obtained from the measured acceleration (steady state) by dividing by the square of the frequency; i.e., via the connection between displacement and acceleration. Indeed, the natural frequency of a proper accelerometer (which measures acceleration) will always be higher than the acceleration one is trying to measure (from which displacement could be obtained), so that (i) the signal is easily observed and/or (ii) no correction for the transfer function involving roll-off is necessary. The closest thing to a displacement measuring device is what historically has been called a 'vibrometer'--where the natural frequency of the instrument is much smaller than the motions to which it responds due to acceleration of the case which houses it. In other words, your comments about displacement are focused in exactly the wrong frequency-direction. (Details for all of this are to be found in "Methods of experimental physics", classical methods, Vol I, ed. by I. Estermann, ed.-in-chief L. Marton, p. 93 (1959). One needs to always keep in mind that we're not dealing with a 'chicken or egg' debate. THE FUNDAMENTAL quantity is acceleration that gives rise to velocity that in turn gives rise to displacement. Going the other way makes no physical sense, according to Newton first, and Einstein last. About your statement 'bodies at rest ....', --this of Newton's famous laws of mechanics (first law, a qualitative statement) is most certainly consistent with his quantitative (quintessential) 2nd law--the basis for describing every classical system that exists. The 2nd law he formulated not in terms of acceleration but rather (genius that he was) in terms of the time rate of change of momentum (which for constant mass gives the famous F = m a. His more general result is able to also describe rocket systems where the mass changes.) Notice that the LAW does not involve velocity, NOR does it involve DISPLACEMENT, except to the extent that acceleration ultimately gives rise to changes in these other state variables. The `god of dynamics' is acceleration; and no other state variable can ever usurp its place of rulership. The challenge to conceptual understanding of these problems is centuries old, and all us physics professionals struggle to correct the misconeptions about motion that our students bring into the classroom. Maybe at the bottom line one has to master the equations Newton gave us (in terms of the calculus describing his 2nd law) before the matter really makes sense. Randall