What is the difference between mass and weight?
Weight
In modern scientific usage, weight and mass are fundamentally different quantities: mass is an intrinsic property of matter, whereas weight is a "force" that results from the action of gravity on matter: it measures how strongly the force of gravity pulls on that matter. However, in most practical everyday situations the word "weight" is used when, strictly, "mass" is meant. For example, most people would say that an object "weighs one kilogram", even though the kilogram is a unit of mass.
Quality (philosophy)
John Locke presented a distinction between primary and secondary qualities in "An Essay Concerning Human Understanding". For Locke, a quality is an idea of a sensation or a perception. Locke further asserts that qualities can be divided in two kinds: primary and secondary qualities. Primary qualities are intrinsic to an object—a thing or a person—whereas secondary qualities are dependent on the interpretation of the subjective mode and the context of appearance. For example, a shadow is a secondary quality. It requires a certain lighting to be applied to an object. For another example, consider the mass of an object. Weight is a secondary quality since, as a measurement of gravitational force, it varies depending on the distance to, and mass of, very massive objects like the Earth, as described by Newton's law. It could be thought that mass is intrinsic to an object, and thus a primary quality. In the context of relativity, the idea of mass quantifying an amount of matter requires caution. The relativistic mass varies for variously traveling observers; then there is the idea of rest mass or invariant mass (the magnitude of the energy-momentum 4-vector), basically a system's relativistic mass in its own rest frame of reference. (Note, however, that Aristotle drew a distinction between qualification and quantification; a thing's quality can vary in degree). Only an isolated system's invariant mass in relativity is the same as observed in variously traveling observers' rest frames, and conserved in reactions; moreover, a system's heat, including the energy of its massless particles such as photons, contributes to the system's invariant mass (indeed, otherwise even an isolated system's invariant mass would not be conserved in reactions); even a cloud of photons traveling in different directions has, as a whole, a rest frame and a rest energy equivalent to invariant mass. Thus, to treat rest mass (and by that stroke, rest energy) as an intrinsic quality distinctive of physical matter raises the question of what is to count as physical matter. Little of the invariant mass of a hadron (for example a proton or a neutron) consists in the invariant masses of its component quarks (in a proton, around 1%) apart from their gluon particle fields; most of it consists in the quantum chromodynamics binding energy of the (massless) gluons (see Quark#Mass).
Mass ratio
where
Mass–energy equivalence
Such a change in mass may only happen when the system is open, and the energy and mass escapes. Thus, if a stick of dynamite is blown up in a hermetically sealed chamber, the mass of the chamber and fragments, the heat, sound, and light would still be equal to the original mass of the chamber and dynamite. If sitting on a scale, the weight and mass would not change. This would in theory also happen even with a nuclear bomb, if it could be kept in an ideal box of infinite strength, which did not rupture or pass radiation. Thus, a 21.5 kiloton () nuclear bomb produces about one gram of heat and electromagnetic radiation, but the mass of this energy would not be detectable in an exploded bomb in an ideal box sitting on a scale; instead, the contents of the box would be heated to millions of degrees without changing total mass and weight. If then, however, a transparent window (passing only electromagnetic radiation) were opened in such an ideal box after the explosion, and a beam of X-rays and other lower-energy light allowed to escape the box, it would eventually be found to weigh one gram less than it had before the explosion. This weight loss and mass loss would happen as the box was cooled by this process, to room temperature. However, any surrounding mass that absorbed the X-rays (and other "heat") would "gain" this gram of mass from the resulting heating, so the mass "loss" would represent merely its relocation. Thus, no mass (or, in the case of a nuclear bomb, no matter) would be "converted" to energy in such a process. Mass and energy, as always, would both be separately conserved.
Conservation of mass
The formula implies that bound systems have an invariant mass (rest mass for the system) less than the sum of their parts, if the binding energy has been allowed to escape the system after the system has been bound. This may happen by converting system potential energy into some other kind of active energy, such as kinetic energy or photons, which easily escape a bound system. The difference in system masses, called a mass defect, is a measure of the binding energy in bound systems – in other words, the energy needed to break the system apart. The greater the mass defect, the larger the binding energy. The binding energy (which itself has mass) must be released (as light or heat) when the parts combine to form the bound system, and this is the reason the mass of the bound system decreases when the energy leaves the system. The total invariant mass is actually conserved, when the mass of the binding energy that has escaped, is taken into account.
Mass–energy equivalence
A consequence of the mass–energy equivalence is that if a body is stationary, it still has some internal or intrinsic energy, called its rest energy, corresponding to its rest mass. When the body is in motion, its total energy is greater than its rest energy, and equivalently its "total mass" (also called relativistic mass in this context) is greater than its rest mass. This rest mass is also called the intrinsic or invariant mass because it remains the same regardless of this motion, even for the extreme speeds or gravity considered in special and general relativity.
Mass (mass spectrometry)
The mass number, also called the nucleon number, is the number of protons and neutrons in an atomic nucleus. The mass number is unique for each isotope of an element and is written either after the element name or as a superscript to the left of an element's symbol. For example, carbon-12 (C) has 6 protons and 6 neutrons.
Mass–energy equivalence
For things and systems made up of many parts, like an atomic nucleus, planet, or star, the relativistic mass is the sum of the relativistic masses (or energies) of the parts, because energies are additive in isolated systems. This is not true in open systems, however, if energy is subtracted. For example, if a system is "bound" by attractive forces, and the energy gained due to the forces of attraction in excess of the work done is removed from the system, then mass is lost with this removed energy. For example, the mass of an atomic nucleus is less than the total mass of the protons and neutrons that make it up, but this is only true after this energy from binding has been removed in the form of a gamma ray (which in this system, carries away the mass of the energy of binding). This mass decrease is also equivalent to the energy required to break up the nucleus into individual protons and neutrons (in this case, work and mass would need to be supplied). Similarly, the mass of the solar system is slightly less than the sum of the individual masses of the sun and planets.
Parasitic mass
Parasitic mass is a rocket, weapons and Personal Rapid Transit (PRT or PodCars) transportation term used to differentiate between the mass of the payload and the moving mass of all other components of the system. It is the mass to which force must be applied to accelerate that is not payload.
Mass balance
or
Kendrick mass
The Kendrick mass is defined by setting the mass of a chosen molecular fragment, typically CH, to an integer value in atomic mass units. It is different from the IUPAC definition, which is based on setting the mass of C isotope to exactly 12 u. The Kendrick mass is often used to identify homologous compounds differing only by a number of base units in high resolution mass spectra. This definition of mass was first suggested in 1963 by chemist Edward Kendrick, and it has been adopted by scientists working in the area of high-resolution mass spectrometry, environmental analysis, proteomics, petroleomics, metabolomics, polymer analysis, etc.
Mass
Mass is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied. The object's mass also determines the strength of its gravitational attraction to other bodies.
Mass–energy equivalence
In relativity, all the energy that moves with an object (that is, all the energy present in the object's rest frame) contributes to the total mass of the body, which measures how much it resists acceleration. Each bit of potential and kinetic energy makes a proportional contribution to the mass. As noted above, even if a box of ideal mirrors "contains" light, then the individually massless photons still contribute to the total mass of the box, by the amount of their energy divided by .
Apparent weight
In physics, apparent weight is a property of objects that corresponds to how heavy an object is. The apparent weight of an object will differ from the weight of an object whenever the force of gravity acting on the object is not balanced by an equal but opposite normal force. By definition, the weight of an object is equal to the magnitude of the force of gravity acting on it. This means that even a "weightless" astronaut in low Earth orbit, with an apparent weight of zero, has almost the same weight as he would have while standing on the ground; this is due to the force of gravity in low Earth orbit and on the ground being almost the same.
Mass in special relativity
C. Alder takes a similarly dismissive stance on mass in relativity. Writing on said subject matter, he says that ""its introduction into the theory of special relativity was much in the way of a historical accident"", noting towards the widespread knowledge of "E=mc" and how the public's interpretation of the equation has largely informed how it is taught in higher education. He instead supposes that the difference between rest and relativistic mass should be explicitly taught, so that students know why mass should be thought of as invariant ""in most discussions of inertia.""
Weight
Discussion of the concepts of heaviness (weight) and lightness (levity) date back to the ancient Greek philosophers. These were typically viewed as inherent properties of objects. Plato described weight as the natural tendency of objects to seek their kin. To Aristotle, weight and levity represented the tendency to restore the natural order of the basic elements: air, earth, fire and water. He ascribed absolute weight to earth and absolute levity to fire. Archimedes saw weight as a quality opposed to buoyancy, with the conflict between the two determining if an object sinks or floats. The first operational definition of weight was given by Euclid, who defined weight as: "weight is the heaviness or lightness of one thing, compared to another, as measured by a balance." Operational balances (rather than definitions) had, however, been around much longer.
Mass
The primary difficulty with Mach's definition of mass is that it fails to take into account the potential energy (or binding energy) needed to bring two masses sufficiently close to one another to perform the measurement of mass. This is most vividly demonstrated by comparing the mass of the proton in the nucleus of deuterium, to the mass of the proton in free space (which is greater by about 0.239%—this is due to the binding energy of deuterium.). Thus, for example, if the reference weight "m" is taken to be the mass of the neutron in free space, and the relative accelerations for the proton and neutron in deuterium are computed, then the above formula over-estimates the mass "m" (by 0.239%) for the proton in deuterium. At best, Mach's formula can only be used to obtain ratios of masses, that is, as "m" /"m" = |a| / |a|. An additional difficulty was pointed out by Henri Poincaré, which is that the measurement of instantaneous acceleration is impossible: unlike the measurement of time or distance, there is no way to measure acceleration with a single measurement; one must make multiple measurements (of position, time, etc.) and perform a computation to obtain the acceleration. Poincaré termed this to be an "insurmountable flaw" in the Mach definition of mass.
Weight
In the 20th century, the Newtonian concepts of absolute time and space were challenged by relativity. Einstein's equivalence principle put all observers, moving or accelerating, on the same footing. This led to an ambiguity as to what exactly is meant by the force of gravity and weight. A scale in an accelerating elevator cannot be distinguished from a scale in a gravitational field. Gravitational force and weight thereby became essentially frame-dependent quantities. This prompted the abandonment of the concept as superfluous in the fundamental sciences such as physics and chemistry. Nonetheless, the concept remained important in the teaching of physics. The ambiguities introduced by relativity led, starting in the 1960s, to considerable debate in the teaching community as how to define weight for their students, choosing between a nominal definition of weight as the force due to gravity or an operational definition defined by the act of weighing.
Invariant mass
Consider the simple case of two-body system, where object A is moving towards another object B which is initially at rest (in any particular frame of reference). The magnitude of invariant mass of this two-body system (see definition below) is different from the sum of rest mass (i.e. their respective mass when stationary). Even if we consider the same system from center-of-momentum frame, where net momentum is zero, the magnitude of the system's invariant mass is not equal to the sum of the rest masses of the particles within it.
Relativistic mechanics
It should be noted that the invariant mass of a system
is different from the sum of the rest masses of the particles of which it is composed due to kinetic energy and binding energy. Rest mass is not a conserved quantity in special relativity unlike the situation in Newtonian physics. However, even if an object is changing internally, so long as it does not exchange energy with surroundings, then its rest mass will not change, and can be calculated with the same result in any frame of reference.
Foot–pound–second system
Together with the fact that the term "weight" is used for the gravitational force in some technical contexts (physics, engineering) and for mass in others (commerce, law), and that the distinction often does not matter in practice, the coexistence of variants of the FPS system causes confusion over the nature of the unit "pound". Its relation to international metric units is expressed in kilograms, not newtons, though, and in earlier times it was defined by means of a mass prototype to be compared with a two-pan balance which is agnostic of local gravitational differences.
Equivalent weight
Equivalent weight (also known as gram equivalent) is the mass of one equivalent, that is the mass of a given substance which will combine with or displace a fixed quantity of another substance. The equivalent weight of an element is the mass which combines with or displaces 1.008 gram of hydrogen or 8.0 grams of oxygen or 35.5 grams of chlorine. These values correspond to the atomic weight divided by the usual valence;.
Equivalent weight
Equivalent weight has the dimensions and units of mass, unlike atomic weight, which is dimensionless. Equivalent weights were originally determined by experiment, but (insofar as they are still used) are now derived from molar masses. Additionally, the equivalent weight of a compound can be calculated by dividing the molecular weight by the number of positive or negative electrical charges that result from the dissolution of the compound.
Earth mass
The relative uncertainty of the geocentric gravitational constant is just , i.e. times smaller than the relative uncertainty for itself. 
For this reason and others, astronomers prefer to use the un-reduced "G" product, or mass ratios
(masses expressed in units of Earth mass or Solar mass) rather than mass in kilograms when referencing and comparing planetary objects.
International System of Units
The early metric systems defined a unit of weight as a base unit, while the SI defines an analogous unit of mass. In everyday use, these are mostly interchangeable, but in scientific contexts the difference matters. Mass, strictly the inertial mass, represents a quantity of matter. It relates the acceleration of a body to the applied force via Newton's law, : force equals mass times acceleration. A force of 1 N (newton) applied to a mass of 1 kg will accelerate it at 1 m/s. This is true whether the object is floating in space or in a gravity field e.g. at the Earth's surface. Weight is the force exerted on a body by a gravitational field, and hence its weight depends on the strength of the gravitational field. Weight of a 1 kg mass at the Earth's surface is ; mass times the acceleration due to gravity, which is 9.81 newtons at the Earth's surface and is about 3.5 newtons at the surface of Mars. Since the acceleration due to gravity is local and varies by location and altitude on the Earth, weight is unsuitable for precision measurements of a property of a body, and this makes a unit of weight unsuitable as a base unit.
Inertia
No physical difference has been found between gravitational and inertial mass in a given inertial frame. In experimental measurements, the two always agree within the margin of error for the experiment. Einstein used the fact that gravitational and inertial mass were equal to begin his general theory of relativity, in which he postulated that gravitational mass was the same as inertial mass, and that the acceleration of gravity is a result of a "valley" or slope in the space-time continuum that masses "fell down". Dennis Sciama later showed that the reaction force produced by the combined gravity of all matter in the universe upon an accelerating object is mathematically equal to the object's inertia, but this would only be a workable physical explanation if, by some mechanism, the gravitational effects operated instantaneously.
Mass fraction (chemistry)
The mass percentage is sometimes called weight percent (wt%) or weight-weight percentage.
Cephalopod size
Mass (often abbreviated WT for 'weight') is reported far less frequently than either mantle or total length, and accurate records do not exist for all of the large cephalopod species. It can also vary widely depending on the state of the specimen at the time of weighing (for example, whether it was measured live or dead, wet or dry, frozen or thawed, pre- or post-fixation, with or without egg mass, and so on).
Mass
The basic SI unit of mass is the kilogram (kg). In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity, but it would still have the same mass. This is because weight is a force, while mass is the property that (along with gravity) determines the strength of this force.
True mass
The term true mass is synonymous with the term mass, but is used in astronomy to differentiate the measured mass of a planet from the lower limit of mass usually obtained from radial velocity techniques. Methods used to determine the true mass of a planet include measuring the distance and period of one of its satellites, advanced astrometry techniques that use the motions of other planets in the same star system, combining radial velocity techniques with transit observations (which indicate very low orbital inclinations), and combining radial velocity techniques with stellar parallax measurements (which also determine orbital inclinations).
Apparent weight
The apparent weight can also differ from weight when an object is "partially or completely immersed in a fluid", where there is an "upthrust" from the liquid that is working against the force of gravity. Another example is the weight of an object or person riding in an elevator. When the elevator begins rising, the object begins exerting a force in the downward direction. If a scale was used, it would be seen that the weight of the object is becoming heavier because of the downward force, changing the apparent weight.
Sprung mass
Sprung mass (or sprung weight), in a vehicle with a suspension, such as an automobile, motorcycle, or a tank, is the portion of the vehicle's total mass that is supported by the suspension, including in most applications approximately half of the weight of the suspension itself. The sprung mass typically includes the body, frame, the internal components, passengers, and cargo, but does not include the mass of the components at the other end of the suspension components (including the wheels, wheel bearings, brake rotors, calipers, and/or continuous tracks (also called caterpillar tracks), if any), which are part of the vehicle's unsprung mass.
Mass–energy equivalence
An object moves with different speed in different frames, depending on the motion of the observer, so the kinetic energy in both Newtonian mechanics and relativity is "frame dependent". This means that the amount of relativistic energy, and therefore the amount of relativistic mass, that an object is measured to have depends on the observer. The "rest mass" is defined as the mass that an object has when it is not moving (or when an inertial frame is chosen such that it is not moving). The term also applies to the invariant mass of systems when the system as a whole is not "moving" (has no net momentum). The rest and invariant masses are the smallest possible value of the mass of the object or system. They also are conserved quantities, so long as the system is isolated. Because of the way they are calculated, the effects of moving observers are subtracted, so these quantities do not change with the motion of the observer.
Mass in special relativity
and of a body at rest
Conservation of mass
For the special type of mass called invariant mass, changing the inertial frame of observation for a whole closed system has no effect on the measure of invariant mass of the system, which remains both conserved and invariant (unchanging), even for different observers who view the entire system. Invariant mass is a system combination of energy and momentum, which is invariant for any observer, because in any inertial frame, the energies and momenta of the various particles always add to the same quantity (the momentum may be negative, so the addition amounts to a subtraction). The invariant mass is the relativistic mass of the system when viewed in the center of momentum frame. It is the minimum mass which a system may exhibit, as viewed from all possible inertial frames.
Standard atomic weight
The use of the name "atomic weight" has attracted a great deal of controversy among scientists. Objectors to the name usually prefer the term "relative atomic mass" (not to be confused with atomic mass). The basic objection is that atomic weight is not a weight, that is the force exerted on an object in a gravitational field, measured in units of force such as the newton or poundal.
Weighing scale
A weighing scale (or weighing balance) is a device to measure weight or mass. These are also known as mass scales, weight scales, mass balance, weight balance, or simply scale, balance, or balance scale.
Molar mass
The term formula weight (F.W.) has a specific meaning when used in the context of DNA synthesis: whereas an individual phosphoramidite nucleobase to be added to a DNA polymer has protecting groups and has its "molecular weight" quoted including these groups, the amount of molecular weight that is ultimately added by this nucleobase to a DNA polymer is referred to as the nucleobase's "formula weight" (i.e., the molecular weight of this nucleobase within the DNA polymer, minus protecting groups).
Mass in special relativity
Relativistic mass and rest mass are both traditional concepts in physics, but the relativistic mass corresponds to the total energy. The relativistic mass is the mass of the system as it would be measured on a scale, but in some cases (such as the box above) this fact remains true only because the system on average must be at rest to be weighed (it must have zero net momentum, which is to say, the measurement is in its center of momentum frame). For example, if an electron in a cyclotron is moving in circles with a relativistic velocity, the mass of the cyclotron+electron system is increased by the relativistic mass of the electron, not by the electron's rest mass. But the same is also true of any closed system, such as an electron-and-box, if the electron bounces at high speed inside the box. It is only the lack of total momentum in the system (the system momenta sum to zero) which allows the kinetic energy of the electron to be "weighed." If the electron is "stopped" and weighed, or the scale were somehow sent after it, it would not be moving with respect to the scale, and again the relativistic and rest masses would be the same for the single electron (and would be smaller). In general, relativistic and rest masses are equal only in systems which have no net momentum and the system center of mass is at rest; otherwise they may be different.
Relativistic mechanics
Taking this formula at face value, we see that in relativity, mass is simply energy by another name (and measured in different units). In 1927 Einstein remarked about special relativity, "Under this theory mass is not an unalterable magnitude, but a magnitude dependent on (and, indeed, identical with) the amount of energy."
Weight
In the operational definition, the weight of an object is the force measured by the operation of weighing it, which is the force it exerts on its support. 
Since, W=downward force on the body by the centre of earth, and there is no acceleration in the body. So, there exists opposite and equal force by the support on the body. Also it is equal to the force exerted by the body on its support because action and reaction have same numerical value and opposite direction.
This can make a considerable difference, depending on the details; for example, an object in free fall exerts little if any force on its support, a situation that is commonly referred to as weightlessness. However, being in free fall does not affect the weight according to the gravitational definition. Therefore, the operational definition is sometimes refined by requiring that the object be at rest. However, this raises the issue of defining "at rest" (usually being at rest with respect to the Earth is implied by using standard gravity). In the operational definition, the weight of an object at rest on the surface of the Earth is lessened by the effect of the centrifugal force from the Earth's rotation.
Mass
Although inertial mass, passive gravitational mass and active gravitational mass are conceptually distinct, no experiment has ever unambiguously demonstrated any difference between them. In classical mechanics, Newton's third law implies that active and passive gravitational mass must always be identical (or at least proportional), but the classical theory offers no compelling reason why the gravitational mass has to equal the inertial mass. That it does is merely an empirical fact.
Weight
The kilogram-force is a non-SI unit of force, defined as the force exerted by a one kilogram mass in standard Earth gravity (equal to 9.80665 newtons exactly). The dyne is the cgs unit of force and is not a part of SI, while weights measured in the cgs unit of mass, the gram, remain a part of SI.
Reduced mass
In physics, the reduced mass is the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics. It is a quantity which allows the two-body problem to be solved as if it were a one-body problem. Note, however, that the mass determining the gravitational force is "not" reduced. In the computation one mass "can" be replaced with the reduced mass, if this is compensated by replacing the other mass with the sum of both masses. The reduced mass is frequently denoted by formula_1 (mu), although the standard gravitational parameter is also denoted by formula_1 (as are a number of other physical quantities). It has the dimensions of mass, and SI unit kg.
Atomic mass
The atomic mass and relative isotopic mass are sometimes confused, or incorrectly used, as synonyms of standard atomic weight (also known as atomic weight) and the standard atomic weight (a particular variety of atomic weight, in the sense that is a standardized atomic weight). However, as noted in the introduction, atomic weight and standard atomic weight represent terms for (abundance-weighted) averages of atomic masses in elemental samples, not for single nuclides. As such, atomic weight and standard atomic weight often differ numerically from relative isotopic mass and atomic mass, and they can also have different units than atomic mass when this quantity is not expressed in unified atomic mass units (see the linked article for atomic weight).
Weighing scale
The balance (also balance scale, beam balance and laboratory balance) was the first mass measuring instrument invented. In its traditional form, it consists of a pivoted horizontal lever with arms of equal lengththe beamand a weighing pan suspended from each arm (hence the plural name ""scales" for a weighing instrument). The unknown mass is placed in one pan and standard masses are added to the other pan until the beam is as close to equilibrium as possible. In precision balances, a more accurate determination of the mass is given by the position of a sliding mass moved along a graduated scale. Technically, a balance compares weight rather than mass, but, in a given gravitational field (such as Earth's gravity), the weight of an object is proportional to its mass, so the standard masses used with balances are usually labeled in units of mass (e.g. g or kg).
Negative mass
General relativity describes gravity and the laws of motion for both positive and negative energy particles, hence negative mass, but does not include the other fundamental forces. On the other hand, the Standard Model describes elementary particles and the other fundamental forces, but it does not include gravity. A unified theory that explicitly includes gravity along with the other fundamental forces may be needed for a better understanding of the concept of negative mass.
Mass versus weight
Normally, the effect of air buoyancy on objects of normal density is too small to be of any consequence in day-to-day activities. For instance, buoyancy’s diminishing effect upon one’s body weight (a relatively low-density object) is that of gravity (for pure water it is about that of gravity). Furthermore, "variations" in barometric pressure will rarely affect one’s weight more than ±1 part in 30,000. However, in metrology (the science of measurement), the precision mass standards for calibrating laboratory scales and balances are manufactured with such accuracy that air density is accounted for to compensate for buoyancy effects. Given the extremely high cost of platinum-iridium mass standards like the International Prototype Kilogram ("the" mass standard in France that defines the magnitude of the kilogram), high-quality "working" standards are made of special stainless steel alloys with densities of about 8,000 kg/m, which occupy greater volume than those made of platinum-iridium, which have a density of about 21,550 kg/m. For convenience, a standard value of buoyancy relative to stainless steel was developed for metrology work and this results in the term "conventional mass". Conventional mass is defined as follows: "For a mass at 20 °C, ‘conventional mass’ is the mass of a reference standard of density 8,000 kg/m which it balances in air with a density of 1.2 kg/m." The effect is a small one, 150 ppm for stainless steel mass standards, but the appropriate corrections are made during the manufacture of all precision mass standards so they have the true labeled mass.
Mass-to-light ratio
In astrophysics and physical cosmology the mass to light ratio, normally designated with the Greek upsilon symbol formula_1, is the quotient between the total mass of a spatial volume (typically on the scales of a galaxy or a cluster) and its luminosity. These ratios are often reported using the value calculated for the Sun as a baseline ratio which is a constant formula_2 = 5133 kg/W equal to a solar mass () divided by a solar luminosity (), (/). The mass to light ratios of galaxies and clusters are all much greater than formula_2 due in part to the fact that most of the matter in these objects does not reside within stars and observations suggest that a large fraction is present in the form of dark matter.
Unsprung mass
In a ground vehicle with a suspension, the unsprung mass (or the unsprung weight) is the mass of the suspension, wheels or tracks (as applicable), and other components directly connected to them, rather than supported by the suspension (the mass of the body and other components supported by the suspension is the sprung mass). Unsprung mass includes the mass of components such as the wheel axles, wheel bearings, wheel hubs, tires, and a portion of the weight of driveshafts, springs, shock absorbers, and suspension links. If the vehicle's brakes are mounted outboard (i.e., within the wheel), their mass (weight) is also considered part of the unsprung mass.
Introduction to general relativity
The equivalence between mass and energy, as expressed by the formula "E" = "mc", is the most famous consequence of special relativity. In relativity, mass and energy are two different ways of describing one physical quantity. If a physical system has energy, it also has the corresponding mass, and vice versa. In particular, all properties of a body that are associated with energy, such as its temperature or the binding energy of systems such as nuclei or molecules, contribute to that body's mass, and hence act as sources of gravity.
Matter
Different fields of science use the term matter in different, and sometimes incompatible, ways. Some of these ways are based on loose historical meanings, from a time when there was no reason to distinguish mass from simply a quantity of matter. As such, there is no single universally agreed scientific meaning of the word "matter". Scientifically, the term "mass" is well-defined, but "matter" can be defined in several ways. Sometimes in the field of physics "matter" is simply equated with particles that exhibit rest mass (i.e., that cannot travel at the speed of light), such as quarks and leptons. However, in both physics and chemistry, matter exhibits both wave-like and particle-like properties, the so-called wave–particle duality.
Weight
Gross weight is a term that is generally found in commerce or trade applications, and refers to the total weight of a product and its packaging. Conversely, net weight refers to the weight of the product alone, discounting the weight of its container or packaging; and tare weight is the weight of the packaging alone.
Mass–energy equivalence
The difference between the rest mass of a bound system and of the unbound parts is the binding energy of the system, if this energy has been removed after binding. For example, a water molecule weighs a little less than two free hydrogen atoms and an oxygen atom. The minuscule mass difference is the energy needed to split the molecule into three individual atoms (divided by ), which was given off as heat when the molecule formed (this heat had mass). Likewise, a stick of dynamite in theory weighs a little bit more than the fragments after the explosion, but this is true only so long as the fragments are cooled and the heat removed. In this case the mass difference is the energy/heat that is released when the dynamite explodes, and when this heat escapes, the mass associated with it escapes, only to be deposited in the surroundings, which absorb the heat (so that total mass is conserved).
Mass
Typically, the mass of objects is measured in relation to that of the kilogram, which is defined as the mass of the "international prototype kilogram" (IPK), a platinum alloy cylinder stored in an environmentally-monitored safe secured in a vault at the International Bureau of Weights and Measures in France. However, the IPK is not convenient for measuring the masses of atoms and particles of similar scale, as it contains trillions of trillions of atoms, and has most certainly lost or gained a little mass over time despite the best efforts to prevent this. It is much easier to precisely compare an atom's mass to that of another atom, thus scientists developed the atomic mass unit (or Dalton). By definition, 1 u is exactly one twelfth of the mass of a carbon-12 atom, and by extension a carbon-12 atom has a mass of exactly 12 u. This definition, however, might be changed by the proposed redefinition of SI base units, which will leave the Dalton very close to one, but no longer exactly equal to it.
Mass–energy equivalence
For a system of particles going off in different directions, the invariant mass of the system is the analog of the rest mass, and is the same for all observers, even those in relative motion. It is defined as the total energy (divided by ) in the center of mass frame (where by definition, the system total momentum is zero). A simple example of an object with moving parts but zero total momentum is a container of gas. In this case, the mass of the container is given by its total energy (including the kinetic energy of the gas molecules), since the system total energy and invariant mass are the same in any reference frame where the momentum is zero, and such a reference frame is also the only frame in which the object can be weighed. In a similar way, the theory of special relativity posits that the thermal energy in all objects (including solids) contributes to their total masses and weights, even though this energy is present as the kinetic and potential energies of the atoms in the object, and it (in a similar way to the gas) is not seen in the rest masses of the atoms that make up the object.
Kilogram
The kilogram is a unit of mass, a property corresponding to the common perception of how "heavy" an object is. Mass is an "inertial" property; that is, it is related to the tendency of an object at rest to remain at rest, or if in motion to remain in motion at a constant velocity, unless acted upon by a force.
Mass
For other situations, such as when objects are subjected to mechanical accelerations from forces other than the resistance of a planetary surface, the weight force is proportional to the mass of an object multiplied by the total acceleration away from free fall, which is called the proper acceleration. Through such mechanisms, objects in elevators, vehicles, centrifuges, and the like, may experience weight forces many times those caused by resistance to the effects of gravity on objects, resulting from planetary surfaces. In such cases, the generalized equation for weight "W" of an object is related to its mass "m" by the equation , where "a" is the proper acceleration of the object caused by all influences other than gravity. (Again, if gravity is the only influence, such as occurs when an object falls freely, its weight will be zero).
Mass
In general relativity, the equivalence principle is the equivalence of gravitational and inertial mass. At the core of this assertion is Albert Einstein's idea that the gravitational force as experienced locally while standing on a massive body (such as the Earth) is the same as the "pseudo-force" experienced by an observer in a non-inertial (i.e. accelerated) frame of reference.
Center of mass
The center of mass plays an important role in astronomy and astrophysics, where it is commonly referred to as the "barycenter". The barycenter is the point between two objects where they balance each other; it is the center of mass where two or more celestial bodies orbit each other. When a moon orbits a planet, or a planet orbits a star, both bodies are actually orbiting around a point that lies away from the center of the primary (larger) body. For example, the Moon does not orbit the exact center of the Earth, but a point on a line between the center of the Earth and the Moon, approximately 1,710 km (1,062 miles) below the surface of the Earth, where their respective masses balance. This is the point about which the Earth and Moon orbit as they travel around the Sun. If the masses are more similar, e.g., Pluto and Charon, the barycenter will fall outside both bodies.
Mass versus weight
Usually, the relationship between mass and weight on Earth is highly proportional; objects that are a hundred times more massive than a one-liter bottle of soda almost always weigh a hundred times more—approximately 1,000 newtons, which is the weight one would expect on Earth from an object with a mass slightly greater than 100 kilograms. Yet, this is not always the case and there are familiar objects that violate this proportionality.
Mass in special relativity
the mass that occurs is the relativistic mass. In other words, the relativistic mass is the proportionality constant between the velocity and the momentum.
Mass in special relativity
If a stationary box contains many particles, it weighs more in its rest frame, the faster the particles are moving. Any energy in the box (including the kinetic energy of the particles) adds to the mass, so that the relative motion of the particles contributes to the mass of the box. But if the box itself is moving (its center of mass is moving), there remains the question of whether the kinetic energy of the overall motion should be included in the mass of the system. The invariant mass is calculated excluding the kinetic energy of the system as a whole (calculated using the single velocity of the box, which is to say the velocity of the box's center of mass), while the relativistic mass is calculated including invariant mass "plus" the kinetic energy of the system which is calculated from the velocity of the center of mass.
Inertia
There is no measurable difference between gravitational mass and inertial mass. The gravitational mass is defined by the quantity of gravitational field material a mass possesses, including its energy. The "inertial mass" (relativistic mass) is a function of the acceleration a mass has undergone and its resultant speed. A mass that has been accelerated to speeds close to the speed of light has its "relativistic mass" increased, and that is why the magnetic field strength in particle accelerators must be increased to force the mass's path to curve. In practice, "inertial mass" is normally taken to be "invariant mass" and so is identical to gravitational mass without the energy component.
Weight management
Body Mass Index (BMI) is a value used to get a general sense of a person's overall mass and is calculated using a person's height and weight. It is more often used than weight alone to determine if an individual is underweight, normal weight, overweight, or obese. The following two equations can used to calculate BMI depending on the units used for height (meters vs. inches) and weight (kilograms vs. pounds):
Mass
However, the mass of the international prototype and its supposedly identical national copies have been found to be drifting over time. It is expected that the re-definition of the kilogram and several other units will occur on May 20, 2019, following a final vote by the CGPM in November 2018. The new definition will use only invariant quantities of nature: the speed of light, the caesium hyperfine frequency, and the Planck constant.
Weight
The introduction of Newton's laws of motion and the development of Newton's law of universal gravitation led to considerable further development of the concept of weight. Weight became fundamentally separate from mass. Mass was identified as a fundamental property of objects connected to their inertia, while weight became identified with the force of gravity on an object and therefore dependent on the context of the object. In particular, Newton considered weight to be relative to another object causing the gravitational pull, e.g. the weight of the Earth towards the Sun.
Pierre Louis Maupertuis
Finally, in 1746 he gave a further paper, the "Loix du mouvement et du repos" ("Laws of movement and rest"), this time to the Berlin Academy of Sciences, which showed that point masses also minimise action. Point masses are bodies that can be treated for the purposes of analysis as being a certain amount of matter (a mass) concentrated at a single point. A major debate in the early part of the eighteenth century concerned the behaviour of such bodies in collisions. Cartesian and Newtonian physicists argued that in their collisions, point masses conserved both momentum and relative velocity. Leibnizians, on the other hand, argued that they also conserved what was called "live force" or "vis viva". This was unacceptable for their opponents for two reasons: the first that live force conservation did not apply to so-called ‘hard’ bodies, bodies that were totally incompressible, whereas the other two conservation principles did; the second was that live force was defined by the product of mass and square of velocity. Why did the velocity appear twice in this quantity, as squaring it suggests? The Leibnizians argued this was simple enough: there was a natural tendency in all matter towards motion, so even at rest, there is an inherent velocity in bodies; when they begin to move, there is a second velocity term corresponding to their actual motion.
Measurement
"Mass" refers to the intrinsic property of all material objects to resist changes in their momentum. "Weight", on the other hand, refers to the downward force produced when a mass is in a gravitational field. In free fall, (no net gravitational forces) objects lack weight but retain their mass. The Imperial units of mass include the ounce, pound, and ton. The metric units gram and kilogram are units of mass.
Weighing scale
Because gravity varies by over 0.5% over the surface of the earth, the distinction between force due to gravity and mass is relevant for accurate calibration of scales for commercial purposes. Usually the goal is to measure the mass of the sample rather than its force due to gravity at that particular location.
Matter
Matter should not be confused with mass, as the two are not the same in modern physics. Matter is a general term describing any 'physical substance'. By contrast, mass is not a substance but rather a quantitative "property" of matter and other substances or systems; various types of mass are defined within physics – including but not limited to rest mass, inertial mass, relativistic mass, mass–energy.
Spheroid
where is the mass of the body defined as
Inertia
Gravitational mass is measured by comparing the force of gravity of an unknown mass to the force of gravity of a known mass. This is typically done with some sort of balance. Equal masses will match on a balance because the gravitational field applies to them equally, producing identical weight. This assumption breaks down near supermassive objects such as black holes and neutron stars due to tidal effects. It also breaks down in weightless environments, because no matter what objects are compared, it will yield a balanced reading.
Mass
The invariant mass of systems is the same for observers in all inertial frames, while the relativistic mass depends on the observer's frame of reference. In order to formulate the equations of physics such that mass values do not change between observers, it is convenient to use rest mass. The rest mass of a body is also related to its energy "E" and the magnitude of its momentum p by the relativistic energy-momentum equation:
Mass versus weight
When an object's weight (its gravitational force) is expressed in "kilograms", this actually refers to the kilogram-force (kgf or kg-f), also known as the "kilopond" (kp), which is a non-SI unit of force. All objects on the Earth's surface are subject to a gravitational acceleration of approximately 9.8 m/s. The General Conference on Weights and Measures fixed the value of standard gravity at precisely 9.80665 m/s so that disciplines such as metrology would have a standard value for converting units of defined mass into defined forces and pressures. Thus the kilogram-force is defined as precisely 9.80665 newtons. In reality, gravitational acceleration (symbol: "g") varies slightly with latitude, elevation and subsurface density; these variations are typically only a few tenths of a percent. See also "Gravimetry".
Mass in special relativity
Mass in special relativity incorporates the general understandings from the laws of motion of special relativity along with its concept of mass–energy equivalence. The word "mass" is given two meanings in special relativity: one ("rest" or "invariant mass", and its equivalent "rest energy") is an invariant quantity which is the same for all observers in all reference frames; the other ("relativistic mass" or the equivalent "total energy" of the body) is dependent on the velocity of the observer. The term "relativistic mass" tends not to be used in particle and nuclear physics and is often avoided by writers on special relativity. They do, however, talk about the (total) energy of a body, which is the equivalent to its relativistic mass, rather than the rest energy equivalent to its rest mass. The measurable inertia and gravitational attraction of a body in a given frame of reference is determined by its relativistic mass, not merely its rest mass. For example, light has zero rest mass but contributes to the inertia (and weight in a gravitational field) of any system containing it.
Electromagnetic mass
The concepts of longitudinal and transverse mass (equivalent to those of Lorentz) were also used by Einstein in his first papers on relativity. However, in special relativity they apply to the entire mass of matter, not only to the electromagnetic part. Later it was shown by physicists like Richard Chace Tolman that expressing mass as the ratio of force and acceleration is not advantageous. Therefore, a similar concept without direction dependent terms, in which force is defined as formula_34, was used as relativistic mass
Mass versus weight
While the "weight" of an object varies in proportion to the strength of the gravitational field, its "mass" is constant (ignoring relativistic effects) as long as no energy or matter is added to the object. For example, although a satellite in orbit (essentially a free-fall) is "weightless," it still retains its mass and inertia. Accordingly, even in orbit, an astronaut trying to accelerate the satellite in any direction will still be required to exert force, and will need to exert ten times as much force to accelerate a 10ton satellite at the same rate as one with a mass of only 1 ton.
Spacetime
Before discussing the experimental evidence regarding these other sources of gravity, we need first to discuss Bondi's distinctions between different possible types of mass: (1) active mass is the mass which acts as the source of a gravitational field; (2) passive mass is the mass which reacts to a gravitational field; (3) inertial mass is the mass which reacts to acceleration.In Newtonian theory,
Invariant mass
If objects within a system are in relative motion, then the invariant mass of the whole system will differ from the sum of the objects' rest masses. This is also equal to the total energy of the system divided by "c". See mass–energy equivalence for a discussion of definitions of mass. Since the mass of systems must be measured with a weight or mass scale in a center of momentum frame in which the entire system has zero momentum, such a scale always measures the system's invariant mass. For example, a scale would measure the kinetic energy of the molecules in a bottle of gas to be part of invariant mass of the bottle, and thus also its rest mass. The same is true for massless particles in such system, which add invariant mass and also rest mass to systems, according to their energy.
Mass in special relativity
The term "relativistic mass" is also sometimes used. This is the sum total quantity of energy in a body or system (divided by "c"). As seen from the center of momentum frame, the relativistic mass is also the invariant mass, as discussed above (just as the relativistic energy of a single particle is the same as its rest energy, when seen from its rest frame). For other frames, the relativistic mass (of a body or system of bodies) includes a contribution from the "net" kinetic energy of the body (the kinetic energy of the center of mass of the body), and is larger the faster the body moves. Thus, unlike the invariant mass, the "relativistic mass" depends on the observer's frame of reference. However, for given single frames of reference and for isolated systems, the relativistic mass is also a conserved quantity.
Inertia
By this formula, the greater its mass, the less a body accelerates under a given force. The masses defined by the above formulas are equal because the latter formula is a consequence of the former, if mass does not depend on time and velocity. Thus, "mass is the quantitative or numerical measure of a body’s inertia, that is of its resistance to being accelerated".
Relativistic mechanics
For isolated systems (closed to all mass and energy exchange), mass never disappears in the center of momentum frame, because energy cannot disappear. Instead, this equation, in context, means only that when any energy is added to, or escapes from, a system in the center-of-momentum frame, the system will be measured as having gained or lost mass, in proportion to energy added or removed. Thus, in theory, if an atomic bomb were placed in a box strong enough to hold its blast, and detonated upon a scale, the mass of this closed system would not change, and the scale would not move. Only when a transparent "window" was opened in the super-strong plasma-filled box, and light and heat were allowed to escape in a beam, and the bomb components to cool, would the system lose the mass associated with the energy of the blast. In a 21 kiloton bomb, for example, about a gram of light and heat is created. If this heat and light were allowed to escape, the remains of the bomb would lose a gram of mass, as it cooled. In this thought-experiment, the light and heat carry away the gram of mass, and would therefore deposit this gram of mass in the objects that absorb them.
Weight
In the ISO International standard ISO 80000-4(2006), describing the basic physical quantities and units in mechanics as a part of the International standard ISO/IEC 80000, the definition of "weight" is given as:
The definition is dependent on the chosen frame of reference. When the chosen frame is co-moving with the object in question then this definition precisely agrees with the operational definition. If the specified frame is the surface of the Earth, the weight according to the ISO and gravitational definitions differ only by the centrifugal effects due to the rotation of the Earth.
Mass (mass spectrometry)
The mass defect used in nuclear physics is different from its use in mass spectrometry. In nuclear physics, the mass defect is the difference in the mass of a composite particle and the sum of the masses of its component parts. In mass spectrometry the mass defect is defined as the difference between the exact mass and the nearest integer mass.
Planetary mass
The difference comes from the way in which planetary masses are calculated. It is impossible to "weigh" a planet, and much less the Sun, against the sort of mass standards which are used in the laboratory. On the other hand, the orbits of the planets give a great range of observational data as to the relative positions of each body, and these positions can be compared to their relative masses using Newton's law of universal gravitation (with small corrections for General Relativity where necessary). To convert these relative masses to Earth-based units such as the kilogram, it is necessary to know the value of the Newtonian gravitational constant, "G". This constant is remarkably difficult to measure in practice, and its value is only known to a precision of one part in ten-thousand.
Electromagnetic mass
This was discussed in connection with the proposal of the electrical origin of matter, so Wilhelm Wien (1900), and Max Abraham (1902), came to the conclusion that the total mass of the bodies is identical to its electromagnetic mass. Wien stated, that if it is assumed that gravitation is an electromagnetic effect too, then there has to be a proportionality between electromagnetic energy, inertial mass, and gravitational mass. When one body attracts another one, the electromagnetic energy store of gravitation is according to Wien diminished by the amount (where formula_7 is the attracted mass, formula_8 the gravitational constant, formula_9 the distance):
Mass–energy equivalence
As is noted above, two different definitions of mass have been used in special relativity, and also two different definitions of energy. The simple equation formula_2 is not generally applicable to all these types of mass and energy, except in the special case that the total additive momentum is zero for the system under consideration. In such a case, which is always guaranteed when observing the system from either its center of mass frame or its center of momentum frame, formula_2 is always true for any type of mass and energy that are chosen. Thus, for example, in the center of mass frame, the total energy of an object or system is equal to its rest mass times formula_4, a useful equality. This is the relationship used for the container of gas in the previous example. It is "not" true in other reference frames where the center of mass is in motion. In these systems or for such an object, its total energy depends on both its rest (or invariant) mass, and its (total) momentum.
Mass versus weight
Objects on the surface of the Earth have weight, although sometimes this weight is difficult to measure. An example is a small object floating in water, which does not appear to have weight since it is buoyed by the water; but it is found to have its usual weight when it is added to water in a container which is entirely supported by and weighed on a scale. Thus, the "weightless object" floating in water actually transfers its weight to the bottom of the container (where the pressure increases). Similarly, a balloon has mass but may appear to have no weight or even "negative" weight, due to buoyancy in air. However the weight of the balloon and the gas inside it has merely been transferred to a large area of the Earth's surface, making the weight difficult to measure. The weight of a flying airplane is similarly distributed to the ground, but does not disappear. If the airplane is in level flight, the same weight-force is distributed to the surface of the Earth as when the plane was on the runway, but spread over a larger area.
Orders of magnitude (mass)
The table below is based on the kilogram (kg), the base unit of mass in the International System of Units (SI). The kilogram is the only standard unit to include an SI prefix ("kilo-") as part of its name. The "gram" (10 kg) is an SI derived unit of mass. However, the "names" of all SI mass units are based on "gram", rather than on "kilogram"; thus 10 kg is a "megagram" (10 g), not a "kilokilogram".
Weight
In commercial and everyday use, the term "weight" is usually used to mean mass, and the verb "to weigh" means "to determine the mass of" or "to have a mass of". Used in this sense, the proper SI unit is the kilogram (kg).
Size
Although the size of an object may be reflected in its mass or its weight, each of these is a different concept. In scientific contexts, mass refers loosely to the amount of "matter" in an object (though "matter" may be difficult to define), whereas weight refers to the force experienced by an object due to gravity. An object with a mass of 1.0 kilogram will weigh approximately 9.81 newtons (newton is the unit of force, while kilogram is the unit of mass) on the surface of the Earth (its mass multiplied by the gravitational field strength). Its weight will be less on Mars (where gravity is weaker), more on Saturn, and negligible in space when far from any significant source of gravity, but it will always have the same mass. Two objects of equal size, however, may have very different mass and weight, depending on the composition and density of the objects. By contrast, if two objects are known to have roughly the same composition, then some information about the size of one can be determined by measuring the size of the other, and determining the difference in weight between the two. For example, if two blocks of wood are equally dense, and it is known that one weighs ten kilograms and the other weighs twenty kilograms, and that the ten kilogram block has a volume of one cubic foot, then it can be deduced that the twenty kilogram block has a volume of two cubic feet.
Weight
Some standard textbooks define weight as a vector quantity, the gravitational force acting on the object. Others define weight as a scalar quantity, the magnitude of the gravitational force. Others define it as the magnitude of the reaction force exerted on a body by mechanisms that keep it in place: the weight is the quantity that is measured by, for example, a spring scale. Thus, in a state of free fall, the weight would be zero. In this sense of weight, terrestrial objects can be weightless: ignoring air resistance, the famous apple falling from the tree, on its way to meet the ground near Isaac Newton, would be weightless.
Kilogram
Gravity and the nature of the Kibble balance, which oscillates test masses up and down against the local gravitational acceleration "g", are exploited so that mechanical power is compared against electrical power, which is the square of voltage divided by electrical resistance. However, "g" varies significantly—by nearly 1%—depending on where on the Earth's surface the measurement is made (see "Earth's gravity"). There are also slight seasonal variations in "g" at a location due to changes in underground water tables, and larger semimonthly and diurnal changes due to tidal distortions in the Earth's shape caused by the Moon and the Sun. Although "g" would not be a term in the "definition" of the kilogram, it would be crucial in the process of measurement of the kilogram when relating energy to power. Accordingly, "g" must be measured with at least as much precision and accuracy as are the other terms, so measurements of "g" must also be traceable to fundamental constants of nature. For the most precise work in mass metrology, "g" is measured using dropping-mass absolute gravimeters that contain an iodine-stabilized helium–neon laser interferometer. The fringe-signal, frequency-sweep output from the interferometer is measured with a rubidium atomic clock. Since this type of dropping-mass gravimeter derives its accuracy and stability from the constancy of the speed of light as well as the innate properties of helium, neon, and rubidium atoms, the 'gravity' term in the delineation of an all-electronic kilogram is also measured in terms of invariants of nature—and with very high precision. For instance, in the basement of the NIST's Gaithersburg facility in 2009, when measuring the gravity acting upon Pt10Ir test masses (which are denser, smaller, and have a slightly lower center of gravity inside the Kibble balance than stainless steel masses), the measured value was typically within 8 ppb of .
Mass–energy equivalence
The relativistic mass of a moving object is larger than the relativistic mass of an object that is not moving, because a moving object has extra kinetic energy. The "rest mass" of an object is defined as the mass of an object when it is at rest, so that the rest mass is always the same, independent of the motion of the observer: it is the same in all inertial frames.
Nuclear binding energy
Mass defect is defined as the difference between the mass of a nucleus, and the sum of the masses of the nucleons of which it is composed. The mass defect is determined by calculating three quantities. These are: the actual mass of the nucleus, the composition of the nucleus (number of protons and of neutrons), and the masses of a proton and of a neutron. This is then followed by converting the mass defect into energy. This quantity is the nuclear binding energy, however it must be expressed as energy per mole of atoms or as energy per nucleon.
Atomic mass
The atomic mass or relative isotopic mass refers to the mass of a single particle, and therefore is tied to a certain specific isotope of an element. The dimensionless standard atomic weight instead refers to the average (mathematical mean) of atomic mass values of a typical naturally-occurring mixture of isotopes for a sample of an element. Atomic mass values are thus commonly reported to many more significant figures than atomic weights. Standard atomic weight is related to atomic mass by the abundance ranking of isotopes for each element. It is usually "about" the same value as the atomic mass of the most abundant isotope, other than what looks like (but is not actually) a rounding difference.
Mass
If |a| is non-zero, the fraction is well-defined, which allows us to measure the inertial mass of "m". In this case, "m" is our "reference" object, and we can define its mass "m" as (say) 1 kilogram. Then we can measure the mass of any other object in the universe by colliding it with the reference object and measuring the accelerations.
Mass number
The mass number (symbol "A", from the German word "Atomgewicht" (atomic weight), also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus. It determines the atomic mass of atoms. Because protons and neutrons both are baryons, the mass number A is identical with the baryon number B as of the nucleus as of the whole atom or ion. The mass number is different for each different isotope of a chemical element. This is not the same as the atomic number ("Z") which denotes the number of protons in a nucleus, and thus uniquely identifies an element. Hence, the difference between the mass number and the atomic number gives the number of neutrons ("N") in a given nucleus: .
Mass
In these frameworks, two kinds of mass are defined: rest mass (invariant mass), and relativistic mass (which increases with velocity). Rest mass is the Newtonian mass as measured by an observer moving along with the object. "Relativistic mass" is the total quantity of energy in a body or system divided by "c". The two are related by the following equation:
Mass (mass spectrometry)
The term packing fraction was defined by Aston as the difference of the measured mass "M" and the nearest integer mass "I" (based on the oxygen-16 mass scale) divided by the quantity comprising the mass number multiplied by ten thousand: