Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: what to call little "g"




Ok. We can't use either common turn of phrase. What to use? The
problem is that there are two contexts for the use of g. One is
freefall, where g really becomes an acceleration. (I prefer using
a(sub)g instead, but that's another story.) Let us name the case were
g should be an acceleration "freefall acceleration."

The other context is in discussing force, eg, W=mg. It always blows
away my students when I point out that g is not an acceleration
here. (In most elementary problems where this first comes up the
mass is at rest! there's clearly no acceleration.) It is the local
gravitational constant which has units Newtons/kilogram. Thus, I name
g in this context the "local gravitational constant."

Let's agree on one thing -- calling it simply "gravity" as most
students strongly yearn to do is the biggest conceptual disaster of
all and promotes the use of "9.8" for all things involving
gravitational interactions.

The central conceptual difficulty here is actually a manifestation of
the equivalence principle and it is worth confronting up front but
nobody does it in any textbook. The g present in free fall is in fact
an acceleration. The g present in W=mg is the local value of the
gravitational field. According to the equivalence principle, they are
the same thing and this follows directly on Galileo's experiments
regarding the equivalence of gravitational and inertial mass.

My personal opinion is that it would be worthwhile to avoid the
introduction of g as an acceleration during the study of kinematics
and postpone it until the time arises to study dynamics. Newton's
Laws (especially the 3rd) tell us to think of forces as interactions
between particles, each of which participates equally in the
interaction, and we can then wonder how they "know" about each other.
This leads to the concept of a field and we can introduce g as the
local value of the gravitational field without having to layer over
it some bizarre kinematic/dynamic hybrid interpretation. Then we can
consider what Galileo has to tell us about the nature of a
gravitational field (as interpreted by Einstein) and we can think of
all forces as local interactions (charge x field) rather than spooky
actions at a distance.

Advantages: avoids confabulation of kinematic and dynamic ideas,
early introduction of field concept rather than smacking them with it
later, gives a local interpretation to Newton's Laws.

Disadvantages: Can't really think of any except that no textbook on
earth does it this way.

The central difficulty is that g has an interpretation as an
acceleration purely due to an idiosyncracy of the gravitational field
but operationally it is a field first which is why it appears in W=mg
even though m may not be accelerating.


(aside: to say that N/kg is the same thing conceptually as m/s^2 is
to agree that torque can be expressed in Joules (N-m). We on phys-l
went through all of that not long ago.)

Not quite. This is not a question of units but rather a question of
the nature of the gravitational field -- it and it alone obeys the
equivalence principle.



PS My next tirade will be on usage like "the tension overcomes the
frictional force" or worse, "gravity overcomes friction..."

I look forward to reading that one. Good luck with the windmills.

John E. Gastineau


Paul J. Camp "The Beauty of the Universe
Assistant Professor of Physics consists not only of unity
Coastal Carolina University in variety but also of
Conway, SC 29528 variety in unity.
pjcamp@csd1.coastal.edu --Umberto Eco
pjcamp@postoffice.worldnet.att.net The Name of the Rose
(803)349-2227
fax: (803)349-2926