Weight is a measure of the centripetal force, or thrust exerted on,
and/or by objects; bodies, or masses of the particles [atoms and
molecules] that comprise the mass of the substances that we call
matter; when they are at rest on the terra firma surface of Earth, or
on a similar planet.
This force is primarily due to gravitation; where all matter is
continuously gravitating toward a common center of mass; at a rate
that varies inversely as the distance separating these centers of
mass; as well as being affected by the centrifugal effect due to the
That is at Earth's equator where the rotation is greatest, the
centrifugal effect is greatest, and therefore causes the centripetal
weight there to be least. Weight will also vary with elevation, and is
less on hills than in valleys, because they are further from Earth's
center than sea level.
Units of weight are units of force: In the International System of
Units (SI), the "modern" metric system, the units of force are the
dyne and the newton. In the foot-pound-second system used in the
United States, units of force customarily include the ounce and the
pound. One pound being equal to 4.448 newtons; which is the weight of
Newton found the "mass" of an object to be equal to it's "bulk and
density, conjointly", as well as being the ratio of its weight [w],
divided by the acceleration at which it will free fall [g] at the
location where it is weighed.
He related this "gravitational mass" [w/g] to mass [m] in general as
being equal to "inertial mass" [f/a]; which is the ratio of the net
force [f], divided by the acceleration [a] that it causes _anywhere_,
_anytime_: Where through algebra: f = wa/g, and w = fg/a: Where the
mass is incidental; since it's just two different ways of saying the
same thing: That mass is a ratio of force to acceleration (and/or
deceleration), and is a measure of inertia.
For commercial and everyday purposes, weight is commonly used to mean
the quantity of matter in an object. When people use weight in this
sense, they measure it on weight scales. The kilogram is the SI's base
unit of mass; where one pound is the weight of 0.454 kilogram.
[This is a rewrite of the World Book's article on weight., and in my
humble opinion is considerably truer.]
A slug at the earth's surface has a weight of about 32.174#. Above the
earth's surface it weighs less and less. Contrary to popular belief ,
below the earth's surface (in a mine or borehole) it has been found
that a mass of matter weighs more than at the surface. The reason is
that weight increases to a maximum as it approaches a common center of
Earth does not _attract matter_ from Earth's center; making it
weightless there: Instead the matter around Earth's center gets
heavier, the closer it is to that center.
In orbit around the earth astronauts feel no weight at all, even
though they are still as massive as they were on the ground. This is
not due to the distance they are from the earth, which may be only a
hundred miles or so. They are weightless because they are in free
fall, as you would be if you fell off a cliff. They don't fall
straight down, however, because they are traveling forward at about 30
times the speed of sound (mach 30), and keep falling around the earth!
Things are less heavy on the moon because they fall about six times
slower there: Mass and/or gravitational inertia are constant because
they are a _ratio_ of their weight, divided by the rate at which they
will free fall; wherever they are. The denominator of the ratio [w/g]
is the acceleration of free fall on the moon, and is only about one
sixth of its value here on Earth: That's what causes things to weigh
only one sixth as much as they do on Earth.
If the people who determined that grams and kilograms were constants
had stopped to think, they'd have realized this; that it's a
scientific fact that weight varies at various locations; in proportion
to the acceleration of free fall [g], which also varies at various
locations: But they didn't; they were in too much of a rush to outdo
the British, and they're still trying. If only they could get the free
people of the U.S. to go along with the scam; but it won't happen:
A few further comments should be added about the force called weight
which is a source of much confusion to many students, and teachers of
physics. Weight is the mutual force exerted between bodies on the
ground and the resisting force exerted by the ground; which restrain
each other from gravitating further toward their common center of
mass; which for all intents and practical purposes is the center of
The force of gravity acting upon an object is sometimes referred to as
the mass of the object. Many students and teachers of physics confuse
weight with mass. The mass of an object refers to the amount of matter
that is contained by the object; the weight of an object is the force
of gravity acting upon that object. Mass is related to "how much stuff
is there" and weight is related to the pull of the Earth (or any other
planet) upon that stuff. The mass of an object (measured in kg) will
be the same no matter where in the universe that object is located.
Mass is never altered by location, the pull of gravity, speed or even
the existence of other forces. For example, a 2-kg object will have a
mass of 2 kg whether it is located on Earth, the moon, or Jupiter; its
mass will be 2 kg whether it is moving or not (at least for all
practical purposes); and its mass will be 2 kg whether it is being
pushed or not.
On the other hand, the weight of an object (measured in Newtons) will
vary according to where in the universe the object is. Weight depends
upon which planet is exerting the force and the distance the object is
from the planet. Weight, being equivalent to the force of gravity, is
dependent upon the value of g. On earth's surface g is 9.8 m/sec^2
(sometimes approximated as 10 m/sec^2). On the moon's surface, g is
1.7 m/sec^2. Go to another planet, and there will be another g value.
Furthermore, the g value is inversely proportional to the distance
from the center of the planet. So if we were to measure g at a
distance of 400 km above the earth's surface, then we would find the g
value to be less than 9.8 m/sec^2:
Always be cautious of the distinction between mass and weight. It is
the source of much confusion for many students and physicists.