Inertial mass

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Inertial mass is a measure of the resistance of an entity to a change in its velocity relative to an inertial frame. The inertial frame does not have to be that of the mass in question; either before or after the measurement.
This 'resistance' is also sometimes called inertia.

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 =1):

m_i a_i1 = m₁ a_1i,

where m_i is the inertial mass of particle i, and a_i1 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 inertial mass of particle i in terms of the assumed measurable mutually induced accelerations a_i1 and a_1i. The remaining constraints on the accelerations, that the above defining equation still holds at different initial distances and when generated by the pairing 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 addition, the requirement that the paired accelerations used are colinear, irrelevant of the direction chosen for the alignment of the particles, verifies that they are measured relative to an inertial frame in a force-free volume.