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*From*: chuck britton <cvbritton@mac.com>*Date*: Mon, 07 Nov 2011 19:58:28 -0400

If you choose to use a rotating reference frame (as we do on the surface of the earth) then we include the v^2/r term in our 'definition' of g.

It affects the direction and the magnitude.

.

At 7:16 PM -0500 11/7/11, Robert Cohen wrote:

I've thought about JD's response below and am a little confused. So it

is *incorrect* to say that GM/r^2 is equal to the strength of the

gravitational field (of the object of mass M at the distance r from its

center)?

Robert A. Cohen, Department of Physics, East Stroudsburg University

570.422.3428 rcohen@esu.edu http://www.esu.edu/~bbq

-----Original Message-----

From: phys-l-bounces@carnot.physics.buffalo.edu

[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of John

Denker

Sent: Thursday, November 03, 2011 4:55 PM

To: Forum for Physics Educators

Subject: [Phys-l] definition of gravity

On 11/03/2011 01:10 PM, Robert Cohen wrote:

When introducing F=mg, is g the gravitational field or is it the local

"acceleration of gravity" (acceleration of an object in the local

frame when the only force acting is gravity)? In other words, does mg

include the centrifugal force associated with the rotating frame of

reference? Might this impact how you introduce the material?

That's an interesting, important question.

... when the only force acting is gravity ...

I'm pretty sure what those words were intended to mean, namely that

"gravity" was intended to be calculated in accordance with the law of

universal gravitation:

"gravity" = G M / r^2 [1]

However, whether or not I'm right about that, I wish to use a different

definition. I recommend *defining* "gravity" to be the acceleration of

the chosen reference frame (as measured by reference to freely-falling

objects).

This is pretty much required for consistency with a modern (post-1915)

understanding of what gravity is, including the equivalence principle.

It is also required for common-sense practical applications such as

architecture.

Let's be clear: The thing that we calculate using equation [1] must not

be considered "the" gravity (except in a few special cases). It is

often the dominant contribution to the gravity, but the other

contributions are quite significant in ordinary real-world applications.

I write:

g_I = G M / r^2 [2]

where the LHS is emphatically not g but rather g_I, which is only one

contribution to g.

For the next level of detail on this, see

http://www.av8n.com/physics/weight.htm

Most textbooks are grotesquely inconsistent about this. They define

gravity one way in the chapter on experiments in the lab frame

(implicitly including all contributions to the frame-

acceleration) and define it another way in the chapter on cosmology

(including only g_I).

It may be that g is numerically equal to g_I for cosmology, if/when we

choose to use a nonrotating reference frame ...

but that's an equation, not a definition. It's a choice, not a law of

nature. For 99% of the practical applications students (and other

folks) see in real life, g is only roughly approximated by g_I.

==================

To summarize:

When introducing F=mg, is g the gravitational field or is it the

local "acceleration of gravity" (acceleration of an object in the

local frame when the only force acting is gravity)?

Yes, both. Those are the same thing, according to the

recommended definitions.

In other words,

does mg include the centrifugal force associated with the rotating

frame of reference? Might this impact how you introduce the

material?

The centrifugal force is *included* in the definition of g,

and in the definition of gravity.

_______________________________________________

Forum for Physics Educators

Phys-l@carnot.physics.buffalo.edu

https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l

_______________________________________________

Forum for Physics Educators

Phys-l@carnot.physics.buffalo.edu

https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l

**References**:**[Phys-l] order of topics (was Newton's first law)***From:*Bill Nettles <bnettles@uu.edu>

**Re: [Phys-l] order of topics (was Newton's first law)***From:*John Denker <jsd@av8n.com>

**Re: [Phys-l] order of topics (was Newton's first law)***From:*"Robert Cohen" <Robert.Cohen@po-box.esu.edu>

**[Phys-l] definition of gravity***From:*John Denker <jsd@av8n.com>

**Re: [Phys-l] definition of gravity***From:*"Robert Cohen" <Robert.Cohen@po-box.esu.edu>

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