How is mass measured?
Mass
In everyday usage, mass and "weight" are often used interchangeably. For instance, a person's weight may be stated as 75 kg. In a constant gravitational field, the weight of an object is proportional to its mass, and it is unproblematic to use the same unit for both concepts. But because of slight differences in the strength of the Earth's gravitational field at different places, the distinction becomes important for measurements with a precision better than a few percent, and for places far from the surface of the Earth, such as in space or on other planets. Conceptually, "mass" (measured in kilograms) refers to an intrinsic property of an object, whereas "weight" (measured in newtons) measures an object's resistance to deviating from its natural course of free fall, which can be influenced by the nearby gravitational field. No matter how strong the gravitational field, objects in free fall are weightless, though they still have mass.
Inertia
Inertial mass is found by applying a known net force to an unknown mass, measuring the resulting acceleration, and applying Newton's Second Law, formula_5. This gives an accurate value for mass, limited only by the accuracy of the measurements. When astronauts need to be measured in the weightlessness of free fall, they actually find their inertial mass in a special chair called a body mass measurement device (BMMD).
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."
Electromagnetic mass
Electromagnetic mass was initially a concept of classical mechanics, denoting as to how much the electromagnetic field, or the self-energy, is contributing to the mass of charged particles. It was first derived by J. J. Thomson in 1881 and was for some time also considered as a dynamical explanation of inertial mass "per se". Today, the relation of mass, momentum, velocity and all forms of energy, including electromagnetic energy, is analyzed on the basis of Albert Einstein's special relativity and mass–energy equivalence. As to the cause of mass of elementary particles, the Higgs mechanism in the framework of the relativistic Standard Model is currently used. In addition, some problems concerning the electromagnetic mass and self-energy of charged particles are still studied.
Mass number
The mass number should also not be confused with the standard atomic weight (also called atomic weight) of an element, which is the ratio of the average atomic mass of the different isotopes of that element (weighted by abundance) to the unified atomic mass unit. The atomic weight is an actual "mass" (made relative, i.e., a ratio), while the mass number is a "counted" number (and so an integer).
Mass (disambiguation)
Mass is a physics term for one of three properties of matter.
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–energy equivalence
The relativistic mass is always equal to the total energy (rest energy plus kinetic energy) divided by . Because the relativistic mass is exactly proportional to the energy, relativistic mass and relativistic energy are nearly synonyms; the only difference between them is the units. If length and time are measured in natural units, the speed of light is equal to 1, and even this difference disappears. Then mass and energy have the same units and are always equal, so it is redundant to speak about relativistic mass, because it is just another name for the energy. This is why physicists usually reserve the useful short word "mass" to mean rest mass, or invariant mass, and not relativistic mass.
Electromagnetic mass
The idea that the principal relations between mass, energy, momentum and velocity can only be considered on the basis of dynamical interactions of matter was superseded, when Albert Einstein found out in 1905 that considerations based on the special principle of relativity require that all forms of energy (not only electromagnetic) contribute to the mass of bodies (mass–energy equivalence). That is, the entire mass of a body is a measure of its energy content by formula_33, and Einstein's considerations were independent from assumptions about the constitution of matter. By this equivalence, Poincaré's radiation paradox can be solved without using "compensating forces", because the mass of matter itself (not the non-electromagnetic aether fluid as suggested by Poincaré) is increased or diminished by the mass of electromagnetic energy in the course of the emission/absorption process. Also the idea of an electromagnetic explanation of gravitation was superseded in the course of developing general relativity.
Matter
In the context of relativity, mass is not an additive quantity, in the sense that one can not add the rest masses of particles in a system to get the total rest mass of the system. Thus, in relativity usually a more general view is that it is not the sum of rest masses, but the energy–momentum tensor that quantifies the amount of matter. This tensor gives the rest mass for the entire system. "Matter" therefore is sometimes considered as anything that contributes to the energy–momentum of a system, that is, anything that is not purely gravity. This view is commonly held in fields that deal with general relativity such as cosmology. In this view, light and other massless particles and fields are all part of "matter".
Measurement
One device for measuring weight or mass is called a weighing scale or, often, simply a "scale". A spring scale measures force but not mass, a balance compares weight, both require a gravitational field to operate. Some of the most accurate instruments for measuring weight or mass are based on load cells with a digital read-out, but require a gravitational field to function and would not work in free fall.
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.
Mass in special relativity
By contrast, the rest mass and invariant masses of systems and particles are "both" conserved "and" also invariant. For example: A closed container of gas (closed to energy as well) has a system "rest mass" in the sense that it can be weighed on a resting scale, even while it contains moving components. This mass is the invariant mass, which is equal to the total relativistic energy of the container (including the kinetic energy of the gas) only when it is measured in the center of momentum frame. Just as is the case for single particles, the calculated "rest mass" of such a container of gas does not change when it is in motion, although its "relativistic mass" does change.
Jupiter mass
Jupiter mass is a common unit of mass in astronomy that is used to indicate the masses of other similarly-sized objects, including the outer planets and extrasolar planets. It may also be used to describe the masses of brown dwarfs, as this unit provides a convenient scale for comparison.
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.
Earth mass
The Henry Cavendish (1798) was the first to attempt to measure the gravitational attraction between two bodies directly in the laboratory.
Earth's mass could be then found by combining two equations; Newton's second law, and Newton's law of universal gravitation.
Energy
Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence. The formula "E" = "mc"², derived by Albert Einstein (1905) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity. In different theoretical frameworks, similar formulas were derived by J.J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information).
Mass spectrometry
Mass spectrometry (MS) is an analytical technique that ionizes chemical species and sorts the ions based on their mass-to-charge ratio. In simpler terms, a mass spectrum measures the masses within a sample. Mass spectrometry is used in many different fields and is applied to pure samples as well as complex mixtures.
Mass
The standard International System of Units (SI) unit of mass is the kilogram (kg). The kilogram is 1000 grams (g), first defined in 1795 as one cubic decimeter of water at the melting point of ice. However, because precise measurement of a decimeter of water at the proper temperature and pressure was difficult, in 1889 the kilogram was redefined as the mass of the international prototype kilogram of cast iron, and thus became independent of the meter and the properties of water.
Mass in special relativity
It is often convenient in calculation that the invariant mass of a system is the total energy of the system (divided by "c") in the COM frame (where, by definition, the momentum of the system is zero). However, since the invariant mass of any system is also the same quantity in all inertial frames, it is a quantity often calculated from the total energy in the COM frame, then used to calculate system energies and momenta in other frames where the momenta are not zero, and the system total energy will necessarily be a different quantity than in the COM frame. As with energy and momentum, the invariant mass of a system cannot be destroyed or changed, and it is thus conserved, so long as the system is closed to all influences. (The technical term is isolated system meaning that an idealized boundary is drawn around the system, and no mass/energy is allowed across it.)
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 .
Gas collecting tube
The mass density of a gas can be measured by using a gas collecting tube, an analytical balance and an aspirator. The mass and volume of a displaced amount of gas are determined: At atmospheric pressure formula_1, the gas collecting tube is filled with the gas to be investigated and the overall mass formula_2 is measured. Then the aspirator sucks out much of the gas yielding a second overall mass formula_3 measurement. (The difference of masses represents the mass (formula_4) of the extracted amount of gas.) Finally, the nearly evacuated gas collecting tube is allowed to suck in an outgassed liquid, usually previously heated water, which is offered under atmospheric pressure formula_1. The gas collecting tube is weighed for a third and last time containing the liquid yielding the value formula_6. (The difference of masses of the nearly evacuated tube and the liquid-containing tube gives the mass (formula_7) of the sucked-in liquid, that took the place of the extracted amount of gas.) The given mass-density formula_8 of the liquid permits to calculate the displaced volume (formula_9). Thus giving mass formula_10 and volume formula_11 of the extracted amount of gas, consequently accessing its mass density (formula_12) under atmospheric pressure
Atomic mass
The atomic mass ("m") is the mass of an atom. Its unit is the unified atomic mass units ("abbr." u) where 1 unified atomic mass unit is defined as of the mass of a single carbon-12 atom, at rest. For atoms, the protons and neutrons of the nucleus account for nearly all of the total mass, and the atomic mass measured in u has nearly the same value as the mass number.
Kibble balance
In addition to measuring "UI", the laboratory must also measure "v" and "g" using experimental methods that do not depend on the definition of mass. The overall precision of "m" depends on the precision of the measurements of "U", "I", "v" and "g". Since there are already methods of measuring "v" and "g" to very high precision, the uncertainty of the mass measurement is dominated by the measurement of "UI", which is the value measured by the Kibble balance.
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".
Mass (mass spectrometry)
The nominal mass for an element is the mass number of its most abundant naturally occurring stable isotope, and for an ion or molecule, the nominal mass is the sum of the nominal masses of the constituent atoms. Isotope abundances are tabulated by IUPAC: for example carbon has two stable isotopes C at 98.9% natural abundance and C at 1.1% natural abundance, thus the nominal mass of carbon is 12. The nominal mass is not always the lowest mass number, for example iron has isotopes Fe, Fe, Fe, and Fe with abundances 6%, 92%, 10%, and 2%, respectively, and a nominal mass of 56. For a molecule, the nominal mass is obtained by summing the nominal masses of the constituent elements, for example water has two hydrogen atoms with nominal mass 1 and one oxygen atom with nominal mass 16, therefore the nominal mass of HO is 18.
Time-of-flight mass spectrometry
Time-of-flight mass spectrometry (TOFMS) is a method of mass spectrometry in which an ion's mass-to-charge ratio is determined via a time of flight measurement. Ions are accelerated by an electric field of known strength. This acceleration results in an ion having the same kinetic energy as any other ion that has the same charge. The velocity of the ion depends on the mass-to-charge ratio (heavier ions of the same charge reach lower speeds, although ions with higher charge will also increase in velocity). The time that it subsequently takes for the ion to reach a detector at a known distance is measured. This time will depend on the velocity of the ion, and therefore is a measure of its mass-to-charge ratio. From this ratio and known experimental parameters, one can identify the ion.
Mass in special relativity
The invariant mass is proportional to the value of the total energy in one reference frame, the frame where the object as a whole is at rest (as defined below in terms of center of mass). This is why the invariant mass is the same as the rest mass for single particles. However, the invariant mass also represents the measured mass when the center of mass is at rest for systems of many particles. This special frame where this occurs is also called the center of momentum frame, and is defined as the inertial frame in which the center of mass of the object is at rest (another way of stating this is that it is the frame in which the momenta of the system's parts add to zero). For compound objects (made of many smaller objects, some of which may be moving) and sets of unbound objects (some of which may also be moving), only the center of mass of the system is required to be at rest, for the object's relativistic mass to be equal to its rest mass.
Mass versus weight
Because mass and weight are separate quantities, they have different units of measure. In the International System of Units (SI), the kilogram is the basic unit of mass, and the newton is the basic unit of force. The non-SI kilogram-force is also a unit of force typically used in the measure of weight. Similarly, the avoirdupois pound, used in both the Imperial system and U.S. customary units, is a unit of mass, and its related unit of force is the pound-force.
Molar mass
While molar masses are almost always, in practice, calculated from atomic weights, they can also be measured in certain cases. Such measurements are much less precise than modern mass spectrometric measurements of atomic weights and molecular masses, and are of mostly historical interest. All of the procedures rely on colligative properties, and any dissociation of the compound must be taken into account.
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 spectrometry
This differential equation is the classic equation of motion for charged particles. Together with the particle's initial conditions, it completely determines the particle's motion in space and time in terms of "m/Q". Thus mass spectrometers could be thought of as "mass-to-charge spectrometers". When presenting data, it is common to use the (officially) dimensionless "m/z", where z is the number of elementary charges ("e") on the ion (z=Q/e). This quantity, although it is informally called the mass-to-charge ratio, more accurately speaking represents the ratio of the mass number and the charge number, "z".
Mass spectrometry
Fourier transform mass spectrometry (FTMS), or more precisely Fourier transform ion cyclotron resonance MS, measures mass by detecting the image current produced by ions cyclotroning in the presence of a magnetic field. Instead of measuring the deflection of ions with a detector such as an electron multiplier, the ions are injected into a Penning trap (a static electric/magnetic ion trap) where they effectively form part of a circuit. Detectors at fixed positions in space measure the electrical signal of ions which pass near them over time, producing a periodic signal. Since the frequency of an ion's cycling is determined by its mass-to-charge ratio, this can be deconvoluted by performing a Fourier transform on the signal. FTMS has the advantage of high sensitivity (since each ion is "counted" more than once) and much higher resolution and thus precision.
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 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 (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 spectrometry
There are several important analyser characteristics. The mass resolving power is the measure of the ability to distinguish two peaks of slightly different "m/z". The mass accuracy is the ratio of the "m/z" measurement error to the true m/z. Mass accuracy is usually measured in ppm or milli mass units. The mass range is the range of "m/z" amenable to analysis by a given analyzer. The linear dynamic range is the range over which ion signal is linear with analyte concentration. Speed refers to the time frame of the experiment and ultimately is used to determine the number of spectra per unit time that can be generated.
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).
Neutron
The mass of a neutron cannot be directly determined by mass spectrometry due to lack of electric charge. However, since the masses of a proton and of a deuteron can be measured with a mass spectrometer, the mass of a neutron can be deduced by subtracting proton mass from deuteron mass, with the difference being the mass of the neutron plus the binding energy of deuterium (expressed as a positive emitted energy). The latter can be directly measured by measuring the energy (formula_1) of the single gamma photon emitted when neutrons are captured by protons (this is exothermic and happens with zero-energy neutrons), plus the small recoil kinetic energy (formula_2) of the deuteron (about 0.06% of the total energy).
Mass
In physical science, one may distinguish conceptually between at least seven different aspects of "mass", or seven physical notions that involve the concept of "mass". Every experiment to date has shown these seven values to be proportional, and in some cases equal, and this proportionality gives rise to the abstract concept of mass. There are a number of ways mass can be measured or operationally defined:
Mass
The force known as "weight" is proportional to mass and acceleration in all situations where the mass is accelerated away from free fall. For example, when a body is at rest in a gravitational field (rather than in free fall), it must be accelerated by a force from a scale or the surface of a planetary body such as the Earth or the Moon. This force keeps the object from going into free fall. Weight is the opposing force in such circumstances, and is thus determined by the acceleration of free fall. On the surface of the Earth, for example, an object with a mass of 50 kilograms weighs 491 newtons, which means that 491 newtons is being applied to keep the object from going into free fall. By contrast, on the surface of the Moon, the same object still has a mass of 50 kilograms but weighs only 81.5 newtons, because only 81.5 newtons is required to keep this object from going into a free fall on the moon. Restated in mathematical terms, on the surface of the Earth, the weight "W" of an object is related to its mass "m" by , where is the acceleration due to Earth's gravitational field, (expressed as the acceleration experienced by a free-falling object).
Mole (unit)
Mass and volume (properties of matter) are often used to quantify a sample of a substance. However, the volume changes with temperature and pressure. Similarly, due to relativistic effects, the mass of a sample changes with temperature, speed or gravity. This effect is very small at low temperature, speed or gravity, but at high speed like in a particle accelerator or theoretical space craft, the change is significant. The amount of substance remains the same regardless of temperature, pressure, speed or gravity, unless a (chemical or nuclear) reaction changes the number of particles.
Mass versus weight
Mass is (among other properties) an "inertial" property; that is, the tendency of an object to remain at constant velocity unless acted upon by an outside force. Under Sir Isaac Newton's -year-old laws of motion and an important formula that sprang from his work, an object with a mass, "m", of one kilogram will accelerate, "a", at one meter per second per second (about one-tenth the acceleration due to earth’s gravity) when acted upon by a force, "F", of one newton.
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.
Molecular mass
Both atomic and molecular masses are usually obtained relative to the mass of the isotope C (carbon 12), which by definition is equal to 12. For example, the molecular mass of methane, whose molecular formula is CH, is calculated as follows:
A more proper term would be "relative molecular mass". However the adjective 'relative' is omitted as it is universally assumed that atomic and molecular masses are relative to the mass of C. Relative atomic and molecular mass values are dimensionless but are given the "unit" Dalton (formerly atomic mass unit) to indicate that the number is equal to the mass of one molecule divided by of the mass of one atom of C. The mass of 1 mol of substance is designated as molar mass. By definition, it has the unit gram.
Conservation of mass
The law of conservation of mass can only be formulated in classical mechanics when the energy scales associated to an isolated system are much smaller than formula_1, where formula_2 is the mass of a typical object in the system, measured in the frame of reference where the object is at rest, and formula_3 is the speed of light.
Density
The density at all points of a homogeneous object equals its total mass divided by its total volume. The mass is normally measured with a scale or balance; the volume may be measured directly (from the geometry of the object) or by the displacement of a fluid. To determine the density of a liquid or a gas, a hydrometer, a dasymeter or a Coriolis flow meter may be used, respectively. Similarly, hydrostatic weighing uses the displacement of water due to a submerged object to determine the density of the object.
Mass-to-charge ratio
In some experiments, the charge-to-mass ratio is the only quantity that can be measured directly. Often, the charge can be inferred from theoretical considerations, so that the charge-to-mass ratio provides a way to calculate the mass of a particle.
Kibble balance
The Kibble balance is a more accurate version of the ampere balance, an early current measuring instrument in which the force between two current-carrying coils of wire is measured and then used to calculate the magnitude of the current. In this new application, the balance will be used in the opposite sense; the current in the coils will be measured using the new standard definition of the Planck constant to "measure mass without recourse to the IPK or any physical object." The balance determines the weight of the object; then the mass can be calculated by accurately measuring the local Earth's gravity (the net acceleration combining gravitational and centrifugal effects) with a gravimeter. Thus the mass of the object is defined in terms of a current and a voltage, as described below—an "electronic kilogram."
Force
Newton's Second Law asserts the direct proportionality of acceleration to force and the inverse proportionality of acceleration to mass. Accelerations can be defined through kinematic measurements. However, while kinematics are well-described through reference frame analysis in advanced physics, there are still deep questions that remain as to what is the proper definition of mass. General relativity offers an equivalence between space-time and mass, but lacking a coherent theory of quantum gravity, it is unclear as to how or whether this connection is relevant on microscales. With some justification, Newton's second law can be taken as a quantitative definition of "mass" by writing the law as an equality; the relative units of force and mass then are fixed.
Mass (mass spectrometry)
The unified atomic mass unit (symbol: u) is the standard unit that is used for indicating mass on an atomic or molecular scale (atomic mass). The dalton (symbol: Da) is equivalent to the unified atomic mass unit. One unified atomic mass unit is approximately the mass of one a single proton or neutron. The unified atomic mass unit has a value of . The "amu" without the "unified" prefix is an obsolete unit based on oxygen, which was replaced in 1961.
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.
Mass-to-charge ratio
The elementary charge-to-electron mass quotient, formula_8, is a quantity in experimental physics. It bears significance because the electron mass "m" is difficult to measure directly, and is instead derived from measurements of the elementary charge e and formula_8. It also has historical significance; the "Q"/"m" ratio of the electron was successfully calculated by J. J. Thomson in 1897—and more successfully by Dunnington, which involves the angular momentum and deflection due to a perpendicular magnetic field. Thomson's measurement convinced him that cathode rays were particles, which were later identified as electrons, and he is generally credited with their discovery.
Gravitational metric system
Nowadays, the mass as a property of an object and its weight, which depends on the gravity of the earth at its position are strictly distinguished. However historically, the kilopond was also called kilogram, and only later the kilogram-mass (today's kilogram) was separated from the kilogram-force (today's kilopond). A kilopond originally referred to the weight of a mass of one kilogram. Since the gravitational acceleration on the surface of the earth can differ, one gets different values for the unit kilopond and its derived units at different locations. To avoid this, the kilopond was first defined at sea-level and a latitude of 45 degrees, since 1902 via the standard gravity of .
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.
Mass versus weight
Engineers and scientists understand the distinctions between mass, force, and weight. Engineers in disciplines involving weight loading (force on a structure due to gravity), such as structural engineering, convert the mass of objects like concrete and automobiles (expressed in kilograms) to a force in newtons (by multiplying by some factor around 9.8; 2 significant figures is usually sufficient for such calculations) to derive the load of the object. Material properties like elastic modulus are measured and published in terms of the newton and pascal (a unit of pressure related to the newton).
Atomic mass
The atomic mass (relative isotopic mass) is defined as the mass of a single atom, which can only be one isotope (nuclide) at a time, and is not an abundance-weighted average, as in the case of relative atomic mass/atomic weight. The atomic mass or relative isotopic mass of each isotope and nuclide of a chemical element is therefore a number that can in principle be measured to a very great precision, since every specimen of such a nuclide is expected to be exactly identical to every other specimen, as all atoms of a given type in the same energy state, and every specimen of a particular nuclide, are expected to be exactly identical in mass to every other specimen of that nuclide. For example, every atom of oxygen-16 is expected to have exactly the same atomic mass (relative isotopic mass) as every other atom of oxygen-16.
Kilogram
Because at any given point on Earth the weight of an object is proportional to its mass, the mass of an object in kilograms is usually measured by comparing its weight to the weight of a standard mass, whose mass is known in kilograms, using a device called a weighing scale. The ratio of the force of gravity on the two objects, measured by the scale, is equal to the ratio of their masses.
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.
Linear density
Consider a long, thin rod of mass formula_1 and length formula_2. To calculate the average linear mass density, formula_3, of this one dimensional object, we can simply divide the total mass, formula_1, by the total length, formula_2:
If we describe the rod as having a varying mass (one that varies as a function of position along the length of the rod, formula_7), we can write:
Each infinitesimal unit of mass, formula_9, is equal to the product of its linear mass density, formula_10, and the infinitesimal unit of length, formula_11:
The linear mass density can then be understood as the derivative of the mass function with respect to the one dimension of the rod (the position along its length formula_13)
Charmed baryons
All particles decay by the strong force. Typically this mean the emission of a pion as it decays down to the comparatively stable . Thus their masses are not usually measured directly, but in terms of their mass differences, m()−m(). This is experimentally easier to measure precisely, and theoretically easier to predict, than the absolute value of the mass.
Proteinogenic amino acid
In mass spectrometry of peptides and proteins, knowledge of the masses of the residues is useful. The mass of the peptide or protein is the sum of the residue masses plus the mass of water (Monoisotopic mass = 18.01056 Da; average mass = 18.0153 Da). The residue masses are calculated from the tabulated chemical formulas and atomic weights. In mass spectrometry, ions may also include one or more protons (Monoisotopic mass = 1.00728 Da; average mass = 1.0074 Da).
§ Monoisotopic mass
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:
Triple beam balance
The triple beam balance is an instrument used to measure mass very precisely. The device has reading error of +/- 0.05 gram. The name refers to the three beams including the middle beam which is the largest size, the front beam which is the medium size, and the far beam which is the smallest size. The difference in size of the beams indicate the difference in weights and reading scale that each beam carry. The reading scale can be enumerated that the middle beam reads in 100 gram increments, the front beam can read from 0 to 10 grams, and the far beam can read in 10 gram increments. The triple beam balance can be used to measure mass directly from the objects, find mass by difference for liquid, and measure out a substance.
Earth mass
The Earth mass is a standard unit of mass in astronomy that is used to indicate the masses of other planets, including rocky terrestrial planets and exoplanets. One Solar mass is close to 333,000 Earth masses.
The Earth mass excludes the mass of the Moon. The mass of the Moon is about 1.2% of that of the Earth, so that the mass of the Earth+Moon system is close to .
Relativistic mechanics
This is the invariant mass of any system which is measured in a frame where it has zero total momentum, such as a bottle of hot gas on a scale. In such a system, the mass which the scale weighs is the invariant mass, and it depends on the total energy of the system. It is thus more than the sum of the rest masses of the molecules, but also includes all the totaled energies in the system as well. Like energy and momentum, the invariant mass of isolated systems cannot be changed so long as the system remains totally closed (no mass or energy allowed in or out), because the total relativistic energy of the system remains constant so long as nothing can enter or leave it.
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.
Conservation of mass
The conservation of both relativistic and invariant mass applies even to systems of particles created by pair production, where energy for new particles may come from kinetic energy of other particles, or from one or more photons as part of a system that includes other particles besides a photon. Again, neither the relativistic nor the invariant mass of totally closed (that is, isolated) systems changes when new particles are created. However, different inertial observers will disagree on the value of this conserved mass, if it is the relativistic mass (i.e., relativistic mass is conserved but not invariant). However, all observers agree on the value of the conserved mass if the mass being measured is the invariant mass (i.e., invariant mass is both conserved and invariant).
Metabolome
Mass spectrometry is an analytical technique that measures the mass-to-charge ratio of molecules. Molecules or molecular fragments are typically charged or ionized by spraying them through a charged field (electrospray ionization), bombarding them with electrons from a hot filament (electron ionization) or blasting them with a laser when they are placed on specially coated plates (matrix assisted laser desorption ionization). The charged molecules are then propelled through space using electrodes or magnets and their speed, rate of curvature, or other physical characteristics are measured to determine their mass-to-charge ratio. From these data the mass of the parent molecule can be determined. Further fragmentation of the molecule through controlled collisions with gas molecules or with electrons can help determine the structure of molecules. Very accurate mass measurements can also be used to determine the elemental formulas or elemental composition of compounds. Most forms of mass spectrometry require some form of separation using liquid chromatography or gas chromatography. This separation step is required to simplify the resulting mass spectra and to permit more accurate compound identification. Some mass spectrometry methods also require that the molecules be derivatized or chemically modified so that they are more amenable for chromatographic separation (this is particularly true for GC-MS). As an analytical technique, MS is a very sensitive method that requires very little sample (<1 ng of material or <10 µL of a biofluid) and can generate signals for 1000s of metabolites from a single sample. MS instruments can also be configured for very high throughput metabolome analyses (100s to 1000s of samples a day). Quantification of metabolites and the characterization of novel compound structures is more difficult by MS than by NMR. LC-MS is particularly amenable to detecting hydrophobic molecules (lipids, fatty acids) and peptides while GC-MS is best for detecting small molecules (<500 Da) and highly volatile compounds (esters, amines, ketones, alkanes, thiols).
Mass-to-charge ratio
The charge-to-mass ratio ("Q"/"m") of an object is, as its name implies, the charge of an object divided by the mass of the same object. This quantity is generally useful only for objects that may be treated as particles. For extended objects, total charge, charge density, total mass, and mass density are often more useful.
Mass in general relativity
where "E" is the total energy of the system, "p" is the total momentum of the system and "c" is the speed of light. Concisely, in fundamental units where formula_2, the mass of a system in special relativity is the norm of its energy–momentum four vector; otherwise, it is formula_3.
Inertia
This was clear at the beginning of the 20th century, before the advent of the theory of relativity. Mass, "m", denoted something like an amount of substance or quantity of matter. At the same time, mass was the quantitative measure of inertia of a body.
Mass attenuation coefficient
The mass attenuation coefficient, mass extinction coefficient, or mass narrow beam attenuation coefficient of the volume of a material characterizes how easily it can be penetrated by a beam of light, sound, particles, or other energy or matter. In addition to visible light, mass attenuation coefficients can be defined for other electromagnetic radiation (such as X-rays), sound, or any other beam that attenuates. The SI unit of mass attenuation coefficient is the square metre per kilogram (). Other common units include cm/g (the most common unit for X-ray mass attenuation coefficients) and mL⋅g⋅cm (sometimes used in solution chemistry). "Mass extinction coefficient" is an old term for this quantity.
Solar mass
The solar mass () is a standard unit of mass in astronomy, equal to approximately . It is used to indicate the masses of other stars, as well as clusters, nebulae, and galaxies. It is equal to the mass of the Sun (denoted by the solar symbol ⊙︎). This equates to about two nonillion (two quintillion in the long scale) kilograms:
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.
Weighing scale
A spring scale measures mass by reporting the distance that a spring deflects under a load. This contrasts to a "balance", which compares the torque on the arm due to a sample weight to the torque on the arm due to a standard reference mass using a horizontal lever. Spring scales measure force, which is the tension force of constraint acting on an object, opposing the local force of gravity. They are usually calibrated so that measured force translates to mass at earth's gravity. The object to be weighed can be simply hung from the spring or set on a pivot and bearing platform.
Electron rest mass
Historically, the mass of the electron was determined directly from combining two measurements. The mass-to-charge ratio of the electron was first estimated by Arthur Schuster in 1890 by measuring the deflection of "cathode rays" due to a known magnetic field in a cathode ray tube. This was before it was even known what cathode rays actually were! It was seven years later that J. J. Thomson showed that cathode rays consist of streams of particles, to be called electrons, and made more precise measurements of their mass-to-charge ratio again using a cathode ray tube.
Mass versus weight
In the physical sciences, the terms "mass" and "weight" are rigidly defined as separate measures, as they are different physical properties. In everyday use, as all everyday objects have both mass and weight and one is almost exactly proportional to the other, "weight" often serves to describe both properties, its meaning being dependent upon context. For example, in retail commerce, the "net weight" of products actually refers to mass, and is expressed in mass units such as grams or ounces (see also "Pound: Use in commerce)". Conversely, the load index rating on automobile tires, which specifies the maximum structural load for a tire in kilograms, refers to weight; that is, the force due to gravity. Before the late 20th century, the distinction between the two was not strictly applied in technical writing, so that expressions such as "molecular weight" (for molecular mass) are still seen.
Mass (mass spectrometry)
The whole number rule states that the masses of the isotopes are integer multiples of the mass of the hydrogen atom. The rule is a modified version of Prout's hypothesis proposed in 1815, to the effect that atomic weights are multiples of the weight of the hydrogen atom.
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:
Mass point geometry
Solution. We may arbitrarily assign the mass of point formula_37 to be formula_38. By ratios of lengths, the masses at formula_39 and formula_40 must both be formula_41. By summing masses, the masses at formula_23 and formula_26 are both formula_44. Furthermore, the mass at formula_31 is formula_46, making the mass at formula_34 have to be formula_48 Therefore formula_35 formula_50 and formula_51. See diagram at right.
Weight
Although Newtonian physics made a clear distinction between weight and mass, the term weight continued to be commonly used when people meant mass. This led the 3rd General Conference on Weights and Measures (CGPM) of 1901 to officially declare "The word "weight" denotes a quantity of the same nature as a "force": the weight of a body is the product of its mass and the acceleration due to gravity", thus distinguishing it from mass for official usage.
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.
Isotope
The mass number is a dimensionless quantity. The atomic mass, on the other hand, is measured using the atomic mass unit based on the mass of the carbon-12 atom. It is denoted with symbols "u" (for unified atomic mass unit) or "Da" (for dalton).
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.
Negative mass
Negative mass is any region of space in which for some observers the mass density is measured to be negative. This could occur due to a region of space in which the stress component of the Einstein stress–energy tensor is larger in magnitude than the mass density. All of these are violations of one or another variant of the positive energy condition of Einstein's general theory of relativity; however, the positive energy condition is not a required condition for the mathematical consistency of the theory.
Center of mass
An experimental method to locate the three-dimensional coordinates of the center of mass begins by supporting the object at three points and measuring the forces, F, F, and F that resist the weight of the object, formula_32 (formula_33 is the unit vector in the vertical direction). Let r, r, and r be the position coordinates of the support points, then the coordinates R of the center of mass satisfy the condition that the resultant torque is zero,
or
This equation yields the coordinates of the center of mass R* in the horizontal plane as,
The center of mass lies on the vertical line L, given by
The three-dimensional coordinates of the center of mass are determined by performing this experiment twice with the object positioned so that these forces are measured for two different horizontal planes through the object. The center of mass will be the intersection of the two lines L and L obtained from the two experiments.
Dimensional analysis
In a similar manner, it is sometimes found useful (e.g., in fluid mechanics and thermodynamics) to distinguish between mass as a measure of inertia (inertial mass), and mass as a measure of quantity (substantial mass). For example, consider the derivation of Poiseuille's Law. We wish to find the rate of mass flow of a viscous fluid through a circular pipe. Without drawing distinctions between inertial and substantial mass we may choose as the relevant variables
Earth mass
The mass of Earth is measured indirectly by determining other quantities such as Earth's density, gravity, or gravitational constant.
The first measurement in the 1770s Schiehallion experiment resulted in a value about 20% too low.
The Cavendish experiment of 1798 found the correct value within 1%.
Uncertainty was reduced to about 0.2% by the 1890s, 
to 0.1% by 1930.
Liquid chromatography–mass spectrometry
The mass spectrum can be used to determine the mass of the analytes, their elemental and isotopic composition, or to elucidate the chemical structure of the sample. MS is an experiment that must take place in gas phase and under vacuum (1.33 * 10 to 1.33 * 10 pascal). Therefore, the development of devices facilitating the transition from samples at higher pressure and in condensed phase (solid or liquid) into a vacuum system has been essential to develop MS as a potent tool for identification and quantification of organic compounds and peptides. MS is now in very common use in analytical laboratories that study physical, chemical, or biological properties of a great variety of compounds. Among the many different kinds of mass analyzers, the ones that find application in LC-MS systems are the quadrupole, time-of-flight (TOF), ion traps, and hybrid quadrupole-TOF (QTOF) analyzers.
Geometrized unit system
Energy and momentum are interpreted as components of the four-momentum vector, and mass is the magnitude of this vector, so in geometric units these must all have the dimension of length. We can convert a mass expressed in kilograms to the equivalent mass expressed in metres by multiplying by the conversion factor "G"/"c". For example, the Sun's mass of in SI units is equivalent to . This is half the Schwarzschild radius of a one solar mass black hole. All other conversion factors can be worked out by combining these two.
Physical organic chemistry
Mass spectrometry is a technique which allows for the measurement of molecular mass and offers complementary data to spectroscopic techniques for structural identification. In a typical experiment a gas phase sample of an organic material is ionized and the resulting ionic species are accelerated by an applied electric field into a magnetic field. The deflection imparted by the magnetic field, often combined with the time it takes for the molecule to reach a detector, is then used to calculate the mass of the molecule. Often in the course of sample ionization large molecules break apart, and the resulting data show a parent mass and a number of smaller fragment masses; such fragmentation can give rich insight into the sequence of proteins and nucleic acid polymers. In addition to the mass of a molecule and its fragments, the distribution of isotopic variant masses can also be determined and the qualitative presence of certain elements identified due to their characteristic natural isotope distribution. The ratio of fragment mass population to the parent ion population can be compared against a library of empirical fragmentation data and matched to a known molecular structure. Combined gas chromatography and mass spectrometry is used to qualitatively identify molecules and quantitatively measure concentration with great precision and accuracy, and is widely used to test for small quantities of biomolecules and illicit narcotics in blood samples. For synthetic organic chemists it is a useful tool for the characterization of new compounds and reaction products.
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.
Slug (unit)
The slug is a derived unit of mass in the weight-based system of measures, most notably within the British Imperial measurement system and in the United States customary measures system. Systems of measure either define mass and derive force or define a base force and derive a mass unit. A slug is defined as the mass that is accelerated by 1 ft/s when a force of one pound (lbf) is exerted on it.
Mass versus weight
In common usage, the mass of an object is often referred to as its weight, though these are in fact different concepts and quantities. In scientific contexts, mass is the amount of "matter" in an object (though "matter" may be difficult to define), whereas weight is the force exerted on an object by gravity. In other words, an object with a mass of 1.0 kilogram will weigh approximately 9.81 newtons on the surface of the Earth (its mass multiplied by the gravitational field strength), since the newton is a unit of force, while the kilogram is a unit of mass. The object's 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.
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 number
The mass number gives an estimate of the isotopic mass measured in atomic mass units (u). For C the isotopic mass is exactly 12, since the atomic mass unit is defined as 1/12 of the mass of C. For other isotopes, the isotopic mass is usually within 0.1 u of the mass number. For example, Cl (17 protons and 18 neutrons) has a mass number of 35 and an isotopic mass of 34.96885. The difference between mass number of an atom and its isotopic mass is known as the mass excess. Mass excess should not be confused with mass defect which is the difference between the mass of an atom and its constituent particles (namely protons, neutrons and electrons).
Mass in general relativity
In special relativity, the invariant mass or "rest mass" ("hereafter simply "mass"") of an isolated system can be defined in terms of the energy and momentum of the system by the relativistic energy–momentum equation:
Jupiter mass
The mass of Jupiter is derived from the measured value called the Jovian mass parameter, which is denoted with "GM". The mass of Jupiter is calculated by dividing "GM" by the constant "G". For celestial bodies such as Jupiter, Earth and the Sun, the value of the "GM" product is known to many orders of magnitude more precisely than either factor independently. The limited precision available for "G" limits the uncertainty of the derived mass. For this reason, astronomers often prefer to refer to the gravitational parameter, rather than the explicit mass. The "GM" products are used when computing the ratio of Jupiter mass relative to other objects.
Mass versus weight
When one stands on a balance-beam-type scale at a doctor’s office, they are having their mass measured directly. This is because balances ("dual-pan" mass comparators) compare the gravitational force exerted on the person on the platform with that on the sliding counterweights on the beams; gravity is the force-generating mechanism that allows the needle to diverge from the "balanced" (null) point. These balances could be moved from Earth's equator to the poles and give exactly the same measurement, i.e. they would not spuriously indicate that the doctor's patient became 0.3% heavier; they are immune to the gravity-countering centrifugal force due to Earth's rotation about its axis. But if you step onto spring-based or digital load cell-based scales (single-pan devices), you are having your weight (gravitational force) measured; and variations in the strength of the gravitational field affect the reading. In practice, when such scales are used in commerce or hospitals, they are often adjusted on-site and certified on that basis, so that the mass they measure, expressed in pounds or kilograms, is at the desired level of accuracy.
In the United States of America the United States Department of Commerce, the Technology Administration, and the National Institute of Standards and Technology (NIST) have defined the use of mass and weight in the exchange of goods under the Uniform Laws and Regulations in the areas of legal metrology and engine fuel quality in NIST Handbook 130.
Acoustic metamaterial
The mass density (or just "density") of a material is defined as mass per unit volume and is expressed in grams per cubic centimeter (g/cm). In all three classic states of matter—gas, liquid, or solid—the density varies with a change in temperature or pressure, and gases are the most susceptible to those changes. The spectrum of densities is wide-ranging: from 10 g/cm for neutron stars, 1.00 g/cm for water to 1.2×10 g/cm for air. Also relevant here are area density which is mass over a (two-dimensional) area, linear density - mass over a one-dimensional line, and relative density, which is a density divided by the density of a reference material, such as water.