# Definition of g-force

## Main Question or Discussion Point

I am having considerable difficulty in finding a precise definition of g-force. My understanding is that it is the acceleration an object would undergo due to just the non-gravitational and non-electromagnetic forces acting on the object. A corollary of this is that an object experiences zero g-force, a.k.a weightlessness, if and only if the vector sum of the non-gravitational and non-electromagnetic forces acting on the object is zero.

According to Wikipedia, weightlessness "is an absence of stress and strain resulting from externally applied mechanical contact-forces, typically normal forces from floors, seats, beds, scales, and the like.".

However these two definitions are contradictory in this simple example: consider a square block acted on by exactly two forces, namely a mechanical contact-force acting on the bottom of the block pointing upward, and a mechanical contact-force acting on the top of the block pointing downward. Here the vector sum of the non-gravitational and non-electromagnetic forces acting on the object is zero, and yet there is clearly no absence of stress and strain.

So the question is: which definition is right?

## Answers and Replies

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DEvens
Education Advisor
Gold Member
Well... Could a bolt on a space station be said to be in free fall? Suppose it is firmly attached to the space station?

Your insistence on "non-gravitational and non-electromagnetic" is very strange. Your insistence on a formulaic definition in this way is also very strange. The fact that you can choose to focus on certain aspects of the context and make the examples look weird isn't particularly helpful.

Your geodesic is the space-time path you would follow if only affected by gravity. Free fall means: Not being pushed off your geodesic.

A.T.
Science Advisor
which definition is right?
Definitions are neither right nor wrong. But usually "weightless" = "free fall".

A corollary of this is that an object experiences zero g-force, a.k.a weightlessness, if and only if the vector sum of the non-gravitational and non-electromagnetic forces acting on the object is zero.
Do you have a reference for that definition?

Dale
Mentor
I am having considerable difficulty in finding a precise definition of g-force.
How about "g force is the acceleration measured by an accelerometer"

HallsofIvy
Science Advisor
Homework Helper
I would disagree that "g-force" can be defined as an acceleration of any kind!

Note: Just to clarify, I am using the terms "zero g-force" and "weightless" interchangeably.

which definition is right?
Definitions are neither right nor wrong.
I'm not sure what you mean. I'm simply looking for a definition of g-force.

But usually "weightless" = "free fall".
I know that, but I'm looking for an exact definition without any "usually"s. That definition doesn't even count an object with no forces acting on it as weightless, for example.

Your insistence on "non-gravitational and non-electromagnetic" is very strange. Your insistence on a formulaic definition in this way is also very strange. The fact that you can choose to focus on certain aspects of the context and make the examples look weird isn't particularly helpful.
The reason it makes sense to excluded gravitational forces is that for small objects gravity acts virtually uniformly, and therefore does not by itself cause stresses or strains. In some cases electromagnetic forces and (now that I think of it) fictitious forces should be excluded for the same reason. I'm not sure what you mean by "formulaic definition". I'm just trying to understand what g-force is. The scenario in the OP is forcing us to define exactly what g-force is, so I would say that it is very helpful.

A corollary of this is that an object experiences zero g-force, a.k.a weightlessness, if and only if the vector sum of the non-gravitational and non-electromagnetic forces acting on the object is zero.
Do you have a reference for that definition?
Yes, see the Wikipedia page on g-force: "The g-force acceleration experienced by an object is due to the vector sum of all non-gravitational and non-electromagnetic forces acting on an object's freedom to move. In practice, as noted, these are surface-contact forces between objects." (I'm not sure what "an object's freedom to move" means though.)

I am having considerable difficulty in finding a precise definition of g-force.
How about "g force is the acceleration measured by an accelerometer"
Wikipedia said:
Weightlessness [zero g-force] is an absence of stress and strain resulting from externally applied mechanical contact-forces, typically normal forces from floors, seats, beds, scales, and the like.
See, this is exactly why I'm having trouble finding a satisfactory definition. Take the scenario I described in the OP. An accelerometer would measure a g-force of zero (correct me if I'm wrong on this), so by your definition the object is weightless. However, according to the Wikipedia definition the object is not weightless. So these two definitions contradict each other in this simple scenario.

I would disagree that "g-force" can be defined as an acceleration of any kind!
That's just a misnomer. g-force is a type of acceleration, as any source will tell you.

Also I forgot to say in the OP: please keep the discussion within the realm of classical mechanics, if possible. Thanks.

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A.T.
Science Advisor
Yes, see the Wikipedia page on g-force: "The g-force acceleration experienced by an object is due to the vector sum of all non-gravitational and non-electromagnetic forces acting on an object's freedom to move. In practice, as noted, these are surface-contact forces between objects."
That's a weird one, because surface-contact forces are electromagnetic too.

According to Wikipedia, weightlessness "is an absence of stress and strain resulting from externally applied mechanical contact-forces, typically normal forces from floors, seats, beds, scales, and the like.".
That is also weird, because if you float in space in a space-suit that is too tight, you have stesses but still "feel weightless" or "zero-g".

I would base it on the accelerometer or proper-acceleration.

I would disagree that "g-force" can be defined as an acceleration of any kind!
That's the problem: "g-force" is an ill-defined hand-wavey term that IS generally used to describe acceleration. As such, trying to pin it down with a rigorous definition seems pointless.

Yes, see the Wikipedia page on g-force: "The g-force acceleration experienced by an object is due to the vector sum of all non-gravitational and non-electromagnetic forces acting on an object's freedom to move. In practice, as noted, these are surface-contact forces between objects." (I'm not sure what "an object's freedom to move" means though.)
That's a weird one, because surface-contact forces are electromagnetic too.
I think by "non-gravitational and non-electromagnetic forces" it means "non-uniformly-acting forces".

I would base it on the accelerometer or proper-acceleration.
OK, I'll stick with that definition. Incidentally, isn't this the same as the Wikipedia definition of g-force above if we replace "non-gravitational and non-electromagnetic forces" by "non-uniformly-acting forces"?

Dale
Mentor
See, this is exactly why I'm having trouble finding a satisfactory definition. Take the scenario I described in the OP. An accelerometer would measure a g-force of zero (correct me if I'm wrong on this), so by your definition the object is weightless. However, according to the Wikipedia definition the object is not weightless. So these two definitions contradict each other in this simple scenario.
Weight and g-force are different. If a working accelerometer measures 0 then the g-force is 0. I don't know of any scenario where the accelerometer definition fails.

HallsofIvy
Science Advisor
Homework Helper
I wasn't arguing about the g-force being defined in terms of acceleration, just with them being treated as the same thing. Clearly, an acceleration is not a force.

Dale
Mentor
I wasn't arguing about the g-force being defined in terms of acceleration, just with them being treated as the same thing. Clearly, an acceleration is not a force.
Yes, it is a rather bad misnomer. Even worse than "escape velocity" which is actually a speed and not a velocity.

The term "g-force" refers to acceleration (measured in multiples of 1 g = 9.8 m/s^2) rather than force (measured in N). Pilots will talk about "pulling 3 g's" to describe the acceleration in a tight turn.

The technical term for "g-force" is "proper acceleration". Which is obviously much clearer, but not nearly as common.