  An important methodological problem of theoretical mechanics related to
inertia is discussed. Analysis Inertia is performed in four-dimensional
Minkowski space-time based on the law of conservation of energy-momentum. This
approach allows us to combine the laws of conservation of momentum and angular
momentum into a single law and separate the forces of inertia that actually
exist in nature from the imaginary forces introduced to simplify calculations
or arising from the transition from one frame of reference to another. From the
energy-momentum tensor, in a non-relativistic approximation, the equation of
balance of inertia forces existing in nature for a moving continuous medium and
a material point in an inertial frame of reference is obtained. It follows from
this equation that the pseudo-Euclidean geometry of our world plays an
important role in the manifestation of inertia forces. The tensor and the
balance equations of all inertia forces in a continuous medium a moving with
angular acceleration are obtained. This allows uniform formulation and
presentation of the original categories and concepts of classical and
relativistic mechanics in educational and scientific literature within the
framework of the current paradigm.
