## PSN-L Email List Message

Subject: instrument physics
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,
(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

```