Mass

Mass is a property of physical objects that, roughly speaking, measures the amount of matter they contain. It is a central concept of classical mechanics and related subjects.

Equivalence of inertial and gravitational masses

The equivalence of inertial and gravitational masses is sometimes referred to as the Galilean equivalence principle or weak equivalence principle. The most important consequence of this equivalence principle applies to freely falling objects. Suppose we have an object with inertial and gravitational masses m and M respectively. If the only force acting on the object comes from a gravitational field g, combining Newton's second law and the gravitational law yields the acceleration

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:K = rac{M}{m} g

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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.)

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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 unlikely to be true; actually, he performed his experiments with balls rolling down inclined planes. Increasingly precise experiments have been performed, such as those performed by Roland Eötvös, using the torsion balance pendulum, in 1889. To date, no deviation from universality, and thus from Galilean equivalence, has ever been found. More precise experimental efforts are still being carried out.

Related Topics:
Galileo - Leaning Tower of Pisa - Inclined plane - Roland Eötvös - Torsion balance pendulum - 1889

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It should be noted that the universality of free fall only applies to systems in which gravity is the only force acting. 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, we all know that the feather will take much longer to reach the ground. This happens because the feather is not really in free fall: the force of air resistance on it is about as strong as the force of gravity. On the other hand, if the experiment is performed in a vacuum, where there is no air resistance, the hammer and the feather should fall at the same rate and reach the ground together. This demonstration was, in fact, carried out in 1971 during the Apollo 15 Moon walk, by Commander David Scott.

Related Topics:
Friction - Air resistance - Negligible - Vacuum - 1971 - Apollo 15 - Moon - David Scott

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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 is 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. All of the predictions of general relativity, such as the curvature of spacetime, are ultimately derived from this principle.

Related Topics:
General theory of relativity - Spacetime

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