A physical quantity determining the inertial and gravitational properties of matter. In classical mechanics inertial mass is the coefficient of proportionality between force and acceleration in Newton's second law, which is a constant for a given body (cf. Newton laws of mechanics). The gravitational mass is defined as the coefficient of proportionality in the law of universal gravitation. According to the principle of equivalence, inertial and gravitational mass are proportional to each other and, in the usual system of units, are equal. In classical physics mass is additive: the mass of a system is equal to the sum of the masses of its parts. In the theory of special relativity mass (the so-called rest mass) can be defined as the coefficient of proportionality in the formula connecting the momentum
where
called the motion mass of the body. By this definition, in relativity theory the momentum and velocity are related by the classical formula
[a1] | M. Jammer, "Concept of mass in classical and modern physics" , Harper & Row (1964) |
[a2] | H. Weyl, "Philosophy of mathematics and natural science" , Princeton Univ. Press (1949) |