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Re: [Phys-L] two very different "gravity" concepts

When you first posted the question, you rejected the name "local". I know it's longer, but what about calling it the "locally observed free fall acceleration"?

And as long as we are naming things, I suggest calling the left side of F = mg the "inferred force of gravity". To me, "inferred" somehow seems more descriptive and less judgmental than "apparent". "Apparent" is often contrasted with "true".

When we teach this to students (months before we discuss universal gravitation), "gravity" is just a name we give to a force whose presence we infer from the observed behavior of objects in free-fall. We BELIEVE Newton's second law and we OBSERVE objects accelerating in freefall...so we infer that there must be a downward force acting on those objects. In fact, we use the direction of that observed freefall (and the associated inferred force) to define what we mean by "downward".

Somewhat related question: later in the course, I may want to teach that there is a small difference between the "downward" we defined with a plumb line and "downward" toward the center of the earth because of the Earth's rotation. Is there a way to measure this experimentally? [I don't always get to this, but still...]


-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of John Denker
Sent: Thursday, January 03, 2013 12:06 AM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] two very different "gravity" concepts

On 01/02/2013 05:33 PM, Bob Sciamanda wrote:
The intended implication is not that the frame is "freely falling" but
that, in the observer's frame, the observed mass m is free to "fall".

Well, even then, that doesn't answer the question that I meant to ask. IMHO
we need a word that describes g, the g that appears in the equation F = m g.
This g depends on what the *frame* is doing, not on what this-or-that mass is
doing.

To illustrate this point, consider two masses and two frames, making four
cases altogether:

falling mass, falling mass,
elevator frame lab frame
g = 0 g = 9.8 m/s/s

mass on lab shelf, mass on lab shelf,
elevator frame lab frame
g = 0 g = 9.8 m/s/s

Note that the elevator is in free fall, and that the shelf is fixed in the lab
frame.

In all cases, g depends on what the frame is doing, not on what this-or-that
mass is doing.

This is the attraction to calling g the framative acceleration of gravity,
because it is frame-relative.

The framative g is distinct from G M / r^2, which is not a frame-relative
quantity.

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