The material point (particle) —the simplest physical model in mechanics — is a body, the size and internal structure of which can be neglected in the conditions of the problem under study. The position of a material point in space is defined as the position of a geometric point. Practically, a material point is understood as having a mass, whose size, shape and rotation can be neglected when solving this problem ^{[1] [2]} .

The mass of a material point is assumed to be constant in time and independent of any features of its movement and interaction with other bodies ^{[3] [4] [5] [6]} .

In the axiomatic approach to the construction of classical mechanics, the following is taken as one of the axioms:

A material point is a geometric point that is associated with a scalar, called a mass: , - vector in Euclidean space, referred to any Cartesian coordinate system. The mass is assumed to be constant, independent of the position of a point in space or of time ^[7] .

If the body participates only in rectilinear motion, then one coordinate axis is enough to determine its position.

Features

The applicability of a material point model to a particular body depends not so much on the size of the body itself, but on the conditions of its movement. In particular, in accordance with the theorem on the motion of the center of mass of the system during translational motion, any solid body can be considered a material point whose position coincides with the center of mass of the body.

The mass, position, speed, and some other physical properties ^{[8] of a} material point at each particular moment in time completely determine its behavior.

Consequences

Mechanical energy can be stored by a material point only in the form of the kinetic energy of its motion in space, and (or) the potential energy of interaction with the field. This automatically means the inability of a material point to deformities (only an absolutely rigid body can be called a material point) and rotation around its own axis and changes in the direction of this axis in space. At the same time, the model of body motion described by a material point, which consists in changing its distance from some instantaneous center of rotation and two Euler angles, which set the direction of the line connecting this point to the center, is extremely widely used in many sections of mechanics.

Restrictions

The limited use of the concept of a material point can be seen from this example: in a rarefied gas at high temperature, the size of each molecule is very small compared to the typical distance between molecules. It would seem that they can be neglected and the molecule is considered a material point. However, this is not always the case: the collocation and rotation of a molecule is an important reservoir of the “internal energy” of a molecule, the “capacity” of which is determined by the size of the molecule, its structure and chemical properties. In a good approximation, a monoatomic molecule can sometimes be viewed as a material point (inert gases, metal vapors, etc.), but even such molecules at a sufficiently high temperature cause electron shells to be excited due to collisions of molecules, followed by flashing.

Notes