is a measure of the resistance of an entity to a change in its velocity
relative to an inertial frame
. Within classical physics
the inertial mass of point particles is defined by means of the following equation for the subsequently described Machian thought experiment
where particle 1 is taken as a unit (m1
- mi ai1 = m1 a1i,
is the inertial mass of particle i, and ai1
is the initial acceleration of particle i, in the direction from particle i to particle 1, in a volume occupied only by particles i and 1, where both particles are initially at rest one distance unit apart. There are no external forces, but the particles exert a force on each other.
The equation defines the inertial mass of particle i in terms of the assumed measurable mutually induced accelerations ai1 and a1i. The remaining constraints on the accelerations, that the above defining equation still holds at different initial distances and when generated by the paring of particles with other than particle 1, can be taken as requirements for the experimental validity of the theory's dynamics, cf. momentum conservation.
In relativity theory, mass increases with velocity, and the rest mass is the inertial mass at v=0.