In physics, mass (from Ancient Greek μᾶζα) commonly refers to any of three properties of matter, which have been shown experimentally to be equivalent: inertial mass, active gravitational mass and passive gravitational mass. In everyday usage, mass is often taken to mean weight, but in scientific use, they refer to different properties.
The inertial mass of an object determines its acceleration in the presence of an applied force. According to Isaac Newton's second law of motion, if a body of mass m is subjected to a force F, its acceleration a is given by F/m.
A body's mass also determines the degree to which it generates or is affected by a gravitational field. If a first body of mass m1 is placed at a distance r from a second body of mass m2, the first body experiences an attractive force F given by
where G is the universal constant of gravitation, equal to 6.67×10−11 kg−1 m3 s−2. This is sometimes referred to as gravitational mass (when a distinction is necessary, M is used to denote the active gravitational mass and m the passive gravitational mass). Repeated experiments since the seventeenth century have demonstrated that inertial and gravitational mass are equivalent; this is entailed in the equivalence principle of general relativity.
Special relativity provides a relationship between the mass of a body and its energy (E = mc2). As a consequence of this relationship, the total mass of a collection of particles may be greater or less than the sum of the masses of the individual particles.
On the surface of the Earth, the weight W of an object is related to its mass m by
where g is the acceleration due to the Earth's gravity, equal to 9.81 m s−2. An object's weight depends on its environment, while its mass does not: an object with a mass of 50 kilograms weighs 491 newtons on the surface of the Earth; on the surface of the Moon, the same object still has a mass of 50 kilograms but weighs only 81.5 newtons.