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Mass is a fundamental concept in physics, roughly corresponding to the intuitive idea of "how much matter there's in an object". Mass is a central concept of classical mechanics and related subjects, and there are several definitions of mass within the framework of relativistic kinematics (see mass in special relativity and mass in General Relativity). In the theory of relativity, the quantity invariant mass, which in concept is close to the classical idea of mass, doesn't vary between single observers in different reference frames.
   In informal everyday usage, mass is more commonly referred to as weight, but in physics and engineering, weight strictly means the size of the gravitational pull on the object; that is, how heavy it is, measured in units of force. In everyday situations, the mass of an object is proportional to its weight, which usually makes it unproblematic to use the same word for both. Distinguishing them becomes important for measurements with a precision better than a few percent, due to slight differences in the strength of the Earth's gravitational field at different places, and is essential when one considers places far from the surface of the Earth, such as in space or on other planets.

Units of mass

In the SI system of units, mass is measured in kilograms, originally defined as the mass of one litre of water. Many other units of mass are also employed, such as: grams (g), tonnes, pounds, ounces, long and short tons, quintals, slugs, atomic mass units, Planck masses, solar masses, and eV/c2.
   Because of the relativistic connection between mass and energy (see mass in special relativity), it's possible to use any unit of energy as a unit of mass instead. For example, the eV energy unit based on the electron volt is normally used as a unit of mass (roughly 1.783 × 10-36 kg) in particle physics. A mass can sometimes also be expressed in terms of inverse length. Here one identifies the mass of a particle with its inverse Compton wavelength (1 mbox g.

This says that the ratio of gravitational to inertial mass of any object is equal to some constant K if and only if all objects fall at the same rate in a given gravitational field. This phenomenon is referred to as the universality of free-fall. (In addition, the constant K can be taken to be 1 by defining our units appropriately.)
   The first experiments demonstrating the universality of free-fall were conducted by Galileo. It is commonly stated that Galileo obtained his results by dropping objects from the Leaning Tower of Pisa, but this is most likely apocryphal; actually, he performed his experiments with balls rolling down inclined planes. Increasingly precise experiments have been performed, such as those performed by Loránd Eötvös, using the torsion balance pendulum, in 1889. To date, no deviation from universality, and thus from Galilean equivalence, has ever been found, at least to the accuracy 1/1012. More precise experimental efforts are still being carried out.
   The universality of free-fall only applies to systems in which gravity is the only acting force. All other forces, especially friction and air resistance, must be absent or at least negligible. For example, if a hammer and a feather are dropped from the same height on Earth, the feather will take much longer to reach the ground; the feather isn't really in free-fall because the force of air resistance upwards against the feather is comparable to the downward force of gravity. On the other hand, if the experiment is performed in a vacuum, in which there's no air resistance, the hammer and the feather should hit the ground at exactly the same time (assuming the acceleration of both objects towards each other, and of the ground towards both objects, for its own part, is negligible). This demonstration is easily done in a high-school laboratory, using two transparent tubes connected to a vacuum pump.
   A stronger version of the equivalence principle, known as the Einstein equivalence principle or the strong equivalence principle, lies at the heart of the general theory of relativity. Einstein's equivalence principle states that it's impossible to distinguish between a uniform acceleration and a uniform gravitational field. Thus, the theory postulates that inertial and gravitational masses are fundamentally the same thing.

Relationship between mass and energy

In special relativity, mass and energy are intimately related, as described by the famous equation E = mc2; see mass-energy equivalence and mass in special relativity.

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