mass in physics, the quantity of matter in a body regardless of its volume or of any forces acting on it. The term should not be confused with weight , which is the measure of the force of gravity (see gravitation ) acting on a body. Under ordinary conditions the mass of a body can be considered to be constant; its weight, however, is not constant, since the force of gravity varies from place to place. There are two ways of referring to mass, depending on the law of physics defining it: gravitational mass and inertial mass. The gravitational mass of a body may be determined by comparing the body on a beam balance with a set of standard masses; in this way the gravitational factor is eliminated. The inertial mass of a body is a measure of the body's resistance to acceleration by some external force. One body has twice as much inertial mass as another body if it offers twice as much force in opposition to the same acceleration. All evidence seems to indicate that the gravitational and inertial masses of a body are equal, as demanded by Einstein's equivalence principle of relativity ; so that at the same location equal (inertial) masses have equal weights. Because the numerical value for the mass of a body is the same anywhere in the world, it is used as a basis of reference for many physical measurements, such as density and heat capacity. According to the special theory of relativity, mass is not strictly constant but increases with the speed according to the formula m = m₀ / 1- v² / c² , where m₀ is the rest mass of the body, v is its speed, and c is the speed of light in vacuum. This increase in mass, however, does not become appreciable until very great speeds are reached. The rest mass of a body is its mass at zero velocity. The special theory of relativity also leads to the Einstein mass-energy relation, E = mc² , where E is the energy, and m and c are the (relativistic) mass and the speed of light, respectively. Because of this equivalence of mass and energy , the law of conservation of energy was extended to include mass as a form of energy.

Mass

One common method of defining mass is to say that it is the quantity of matter an object possesses. For example, a small rock has a fixed, unchanging quantity of matter. If you were to take that rock to the Moon, to Mars, or to any other part of the universe, it would have the same quantity of matter—the same mass—as it has on Earth.

Mass is sometimes confused with weight. Weight is defined as the gravitational attraction on an object by some body, such as Earth or the Moon. The rock described above would have a greater weight on Earth than on the Moon because Earth exerts a greater gravitational attraction on bodies than does the Moon.

Mass and the second law

A more precise definition of mass can be obtained from Newton's second law of motion. According to that law—and assuming that the object in question is free to move horizontally without friction—if a constant force is applied to an object, that object will gain speed. For example, if you hit a ball with a hammer (the constant force), the ball goes from a zero velocity (when it is at rest) to some speed as it rolls across the ground. Mathematically, the second law can be written as F = m · a, where F is the force used to move an object, m is the mass of the object, and a is the acceleration, or increase in speed of the object.

Newton's second law says that the amount of speed gained by an object when struck by a force depends on the quantity of matter in the object. Suppose that you strike a bowling ball and a golf ball with the same force. The golf ball gains a great deal more speed than does the bowling ball because it takes a greater force to get the bowling ball moving than it does to get the golf ball moving.

This fact provides another way of defining mass. Mass is the increase in speed of an object provided by some given force. Or, one can solve the equation above for m, the mass of an object, to get m = F ÷ a. A kilogram, for example, can be defined as the mass that increases its speed at the rate of one meter per second when it is struck by a force of one newton.

Units of mass

In the SI system of measurement (the International System of Units), the fundamental unit of mass is the kilogram. A smaller unit, the gram, is also used widely in many measurements. In the English system, the unit of mass is the slug. A slug is equal to 14.6 kilograms.

Scientists and nonscientists alike commonly convert measurements between kilogram and pounds, not kilograms and slugs. Technically, though, a kilogram/pound conversion is not correct since kilogram is a measure of mass and pound a measure of weight. However, such measurements and such conversions almost always involve observations made on Earth's surface where there is a constant ratio between mass and weight.

[See also Acceleration; Density; Force; Laws of motion; Matter, states of ]

mass A measure of the amount of matter in a body. Mass gives rise to the inertia of an object, i.e. its resistance to change in its motion or state of rest; this is known as the inertial mass. It also produces a gravitational force (see Gravitation). Although mass is formally defined in terms of its inertia, it is usually measured by the effects of its gravitation. The equivalence principle of general relativity asserts that inertial mass and gravitational mass are equal for all bodies, and experiments have verified this equality to one part in 10¹². The weight of a body is the force by which it is gravitationally attracted to the Earth. Although the terms ‘mass’ and ‘weight’ are often used interchangeably on Earth, in space a body may be weightless but still retain its inertia, i.e. it still requires a force to change its motion. According to the special theory of relativity, the mass of a body increases as its velocity approaches that of light. At the speed of light itself the mass would be infinite.

inertial mass A measure of a body's resistance to a change in its velocity or state of rest. Inertia is a direct property of the mass of a body: the greater the mass, the greater its inertia. Although mass is formally defined in terms of its inertia, it is usually measured by gravitation. See also Gravitational Mass.

gravitational mass A measure of the quantity of matter in a body. It is measured in kilograms. Mass determines the strength of the gravitational force exerted by an object. See also inertial mass.