A material point is an infinitely small body with a mass, the shape of which can be neglected. This is the simplest, idealized body, the geometric dimensions of which are small, and only 3 coordinates are needed to determine it in space. The rotation of the material point is also neglected. It is believed that inside a material point, there are no forces. It does not shrink, does not stretch, but is absolutely elastic. The mass of a material point is constant in time, and does not depend on any other conditions.
Figure 1 - replacement of the body by a material point.
The concept of a material point is introduced into mechanics to simplify the description of the motion of material bodies. A body of arbitrary shape, which already has elasticity, can perform both translational and rotational motion. It may also deform. That is, separate points of the body, in addition to moving along with the body, also make a movement relative to it. In the general case, the motion of an arbitrary-shaped body is quite complex and difficult to describe.
Just to simplify the description of such a movement, the concept of a material point is introduced. It is believed that it has the mass of the described body, but infinitesimal dimensions. It only performs forward movement. The material point is used to define the center of mass. This is precisely the point that has the mass distributed over the volume of the body.
Figure 2 - material point.
It is clear that one cannot simply take and replace the body of a complex handicap with an extremely simplified model. For this, certain conditions must be met. The main of which is: the dimensions of the body must be many times smaller than the distance it travels. Also, an important factor affecting the possibility of replacing a real body with a simplified model is the conditions of the experiment and the expected result.
Let's assume that according to the conditions of the experiment, it is necessary to determine the time during which the train will cover the distance from point A to point B, knowing its speed. In this case, we do not care what shape the train has, and how many cars the train consists of. Because we know its speed. It can be represented as a material point. But if we need to determine the air resistance exerted by the train when moving at high speeds. To represent it as a material point is meaningless. Since the result of this experiment depends on the shape of the train.
And what to do in the case when the body cannot be represented as a material point. Due to the fact that it has a complex shape. And its separate parts move not only with linear, but also with angular speed. Then the body is represented as a sum of individual material points. Which will only make forward movement.
MATERIAL POINT MATERIAL POINT, a concept introduced in mechanics to designate a body, the size and shape of which can be neglected. The position of a material point in space is defined as the position of a geometric point. A body can be considered a material point in cases where it moves translationally over large (compared to its size) distances; for example, the Earth with a radius of about 6.4 thousand km is a material point in its annual movement around the Sun (the radius of the orbit - the so-called ecliptic - is about 150 million km). Similarly, the concept of a material point is applicable if the rotational part of the motion of the body can be ignored under the conditions of the problem under consideration (for example, the daily rotation of the Earth can be neglected when studying the annual motion).Modern encyclopedia. 2000.
Material point
Based on the possibility of localization of physical objects in time and space, in classical mechanics, the study of the laws of displacement begins with the simplest case. This case is the movement of a material point. With the schematic idea of an elementary particle, analytical mechanics forms the prerequisites for the presentation of the basic laws of dynamics.
A material point is an object that has an infinitesimal size and finite mass. This idea is fully consistent with the concept of the discreteness of matter. Previously, physicists tried to define it as a set of elementary particles in a state of movement. In this regard, the material point in its dynamics has become just the tool necessary for theoretical constructions.
The dynamics of the object under consideration proceeds from the inertial principle. According to him, a material point, not under the influence of external forces, retains its state of rest (or movement) over time. This provision is strictly enforced.
In accordance with the principle of inertia, a material point (free) moves uniformly and in a straight line. Considering the special case in which the speed is zero, we can say that the object maintains a state of rest. In this regard, it can be assumed that the influence of a certain force on the object under consideration is reduced simply to a change in its speed. The simplest hypothesis is the assumption that the change in speed possessed by a material point is directly proportional to the indicator of the force acting on it. In this case, the proportionality coefficient decreases with increasing inertia.
It is natural to characterize a material point with the help of the value of the coefficient of inertia - mass. In this case, the main law of the dynamics of an object can be formulated as follows: the reported acceleration at each moment of time is equal to the ratio of the force that acts on the object to its mass. The presentation of kinematics thus precedes the presentation of dynamics. Mass, which in dynamics characterizes a material point, is introduced a posteriori (from experience), while the presence of a trajectory, position, acceleration, velocity is admitted a priori.
In this regard, the equations of the dynamics of an object state that the product of the mass of the object under consideration and any of the components of its acceleration is equal to the corresponding component of the force acting on the object. Assuming that the force is a known function of time and coordinates, the determination of the coordinates for a material point in accordance with time is carried out using three ordinary differential equations of the second order in time.
In accordance with the well-known theorem from the course of mathematical analysis, the solution of the indicated system of equations is uniquely determined by setting the coordinates, as well as their first derivatives in some initial time interval. In other words, with a known position of a material point and its speed at a certain moment, it is possible to accurately determine the nature of its movement in all future periods.
As a result, it becomes clear that the classical dynamics of the object under consideration is in absolute accordance with the principle of physical determinism. According to him, the future state (position) of the material world can be predicted completely if there are parameters that determine its position at a certain previous moment.
Due to the fact that the size of a material point is infinitely small, its trajectory will be a line occupying only a one-dimensional continuum in three-dimensional space. In each section of the trajectory, there is a certain value of the force that sets the movement in the next infinitesimal time interval.
/ answers in physics, not all
Question
Mechanics, kinematics, dynamics (definition, scope of tasks).
Answer
Mechanics- the science of the general laws of motion of bodies.
The bodies around us move relatively slowly. Therefore, their movements obey Newton's laws. Thus, the field of application of classical mechanics is very extensive. And in this area, humanity will always use Newton's laws to describe any movement of the body.
Kinematics- This is a branch of mechanics that studies how to describe movements and the relationship between the quantities that characterize these movements.
To describe the movement of a body means to indicate a way to determine its position in space at any given time.
Question
Mechanical motion, reference body, frame of reference, ways to indicate the position of a material point on the coordinate plane, the concept of a kinematic equation of a material point.
Answer
Mechanical movement called the movement of bodies or parts of bodies in space relative to each other over time.
The body relative to which the motion is considered is called reference body.
The totality of the body of reference, the coordinate system associated with it and the clock is called reference system.
Mathematically, the movement of a body (or a material point) with respect to a chosen frame of reference is described by equations that establish how the coordinates that determine the position of the body (point) in this frame of reference change over time t. These equations are called the equations of motion. For example, in Cartesian coordinates x, y, z, the movement of a point is determined by the equations , , .
Methods for specifying the position of a material point on the coordinate plane
Specifying the position of a point using coordinates. From the course of mathematics, you know that the position of a point on a plane can be specified using two numbers, which are called the coordinates of this point. For this, as is known, it is possible to draw two intersecting mutually perpendicular axes on the plane, for example, the axes OX and OY. The point of intersection of the axes is called the origin, and the axes themselves are called the coordinate axes.
The coordinates of the point M1 (Fig. 1.2) are equal to Xj = 2, yx - 4; the coordinates of the point M2 are x2 = -2.5, y2 = -3.5.
The position of the point M in space relative to the reference body can be set using three coordinates. To do this, it is necessary to draw three mutually perpendicular axes OX, OY, OZ through the selected point of the reference body. In the resulting coordinate system, the position of the point will be determined by three coordinates x, y, z.
If the number x is positive, then the segment is plotted in the positive direction of the OX axis (Fig. 1.3) (x - O A). If the number x is negative, then the segment is laid in the negative direction of the x-axis. From the end of this segment, a straight line is drawn parallel to the OY axis, and on this straight line a segment is laid off from the OX axis corresponding to the number y (y \u003d AB) - in the positive direction of the OY axis, if M is positive, and in the negative direction of the OY axis, if y is negative. 
Further, from point B of another from-U, the cutting is carried out in a straight line parallel to the OZ axis. On this line from the XOY coordinate plane, a segment is plotted corresponding to the number 2. Direction, fig. 1.4 in which this segment is postponed is determined in the same way as in previous cases.
The end of the third segment is the point whose position is given by the coordinates x, y, z.
To determine the coordinates of a given point, it is necessary to carry out in reverse order the operations that we carried out, finding the position of this point by its coordinates.
Specifying the position of a point using a radius vector. The position of a point can be set not only with the help of coordinates, but also with the help of a radius vector. A radius vector is a directed segment drawn from the origin to a given point. _ 
The radius vector is usually denoted by the letter r. The length of the radius vector, or, which is the same thing, its module (Fig. 1.4), is the distance from the origin to the point M.
The position of a point will be determined using the radius vector only if its modulus (length) and direction in space are known. Only under this condition will we know in which direction from the origin a segment of length r should be drawn in order to determine the position of the point.
So, the position of a point in space is determined by its coordinates or its radius vector.
The module and direction of any vector are found by its projections on the coordinate axes. To understand how this is done, it is first necessary to answer the question: what is meant by the projection of a vector onto an axis? 
Let us drop from the beginning A and the end B of the vector a the perpendiculars to the OX axis.
Points Aj and Bj are projections, respectively, of the beginning and end of the vector a onto this axis.
The projection of the vector a on any axis is the length of the segment A1B1 between the projections of the beginning and end of the vector on this axis, taken with the sign "+" or "-".
We will denote the projection of a vector by the same letter as the vector, but, firstly, without an arrow above it and, secondly, with an index at the bottom indicating which axis the vector is projected onto. So, ax and ay are the projections of the vector a on the coordinate axes OX and OY.
According to the definition of the projection of a vector onto an axis, one can write: ax = ± I AjEJ.
The projection of a vector onto an axis is an algebraic quantity. It is expressed in the same units as the modulus of the vector.
Let us agree to consider the projection of a vector onto the axis as positive if one must go from the projection of the beginning of the vector to the projection of its end in the positive direction of the projection axis. Otherwise (see Fig. 1.5) it is considered negative.
From figures 1.5 and 1.6 it is easy to see that the projection. vector on the axis will be positive when the vector makes an acute angle with the direction of the projection axis, and negative when the vector makes an obtuse angle with the direction of the projection axis.
The position of a point in space can be specified using coordinates or a radius vector connecting the origin and the point.
WAYS OF DESCRIPTION OF MOVEMENT. REFERENCE SYSTEM
If the body can be considered a point, then to describe its motion, one must learn to calculate the position of the point at any time relative to the selected reference body. 
There are several ways to describe, or, what is the same, task, the movement of a point. Let's take a look at two of the most commonly used.
coordinate way. We will set the position of the point using coordinates (Fig. 1.7). If a point moves, then its coordinates change over time.
Since the coordinates of a point depend on time, we can say that they are functions of time. Mathematically, this is usually written as
(1.1)
Equations (1.1) are called kinematic equations of motion of a point written in coordinate form. If they are known, then for each moment of time we will be able to calculate the coordinates of the point, and, consequently, its position relative to the selected reference body. The form of equations (1.1) for each specific motion will be quite definite.
The line along which a point moves in space is called a trajectory.
Depending on the shape of the trajectory, all movements of the point are divided into rectilinear and curvilinear. If the trajectory is a straight line, the movement of the point is called rectilinear, and if the curve is curvilinear.
Vector way. The position of a point can be specified, as is well known, with the help of a radius vector. When a material point moves, the radius vector that determines its position changes over time (turns and changes length; Fig. 1.8), i.e. is a function of time: 
The last equation is the law of motion of a point written in vector form. If it is known, then we can calculate the radius vector of a point for any moment of time, and therefore determine its position. Thus, specifying three scalar equations (1.1) is equivalent to specifying one vector equation (1.2).
Kinematic equations of motion, written in coordinate or vector form, allow you to determine the position of a point at any time.
Question
Trajectory, path, movement.
Answer
The trajectory of a material point is a line in space, which is a set of points in which a material point was, is or will be when it moves in space relative to the selected reference system. It is essential that the concept of a trajectory has a physical meaning even in the absence of any movement along it. The concept of a trajectory can be illustrated quite clearly by a bobsleigh track. (If, according to the conditions of the problem, its width can be neglected). And it is the track, and not the bean itself.
It is customary to describe the trajectory material point in a predetermined coordinate system using a radius vector, the direction, length and starting point of which depend on time. In this case, the curve described by the end of the radius vector in space can be represented as conjugate arcs of different curvature, which are generally in intersecting planes. In this case, the curvature of each arc is determined by its radius of curvature directed towards the arc from the instantaneous center of rotation, which is in the same plane as the arc itself. Moreover, a straight line is considered as the limiting case of a curve, the radius of curvature of which can be considered equal to infinity. And therefore, the trajectory in the general case can be represented as a set of conjugate arcs.
It is essential that the shape of the trajectory depends on the reference system chosen to describe the motion of a material point. Thus, rectilinear uniformly accelerating motion in one inertial frame will generally be parabolic in another uniformly moving inertial reference frame.
material speed point is always tangent to the arc used to describe the point's path. In this case, there is a relationship between the magnitude of the speed, normal acceleration and the radius of curvature of the trajectory at a given point:
However, not every movement with a known speed along a curve of a known radius and the normal (centripetal) acceleration found using the above formula is associated with the manifestation of a force directed along the normal to the trajectory (centripetal force). Thus, the acceleration of any of the stars found from photographs of the daily motion of the luminaries does not at all indicate the existence of a force that causes this acceleration, attracting it to the Polar Star, as the center of rotation.
Path - the length of the section of the trajectory of a material point in physics.
Displacement (in kinematics) is a change in the location of a physical body in space relative to the selected frame of reference. Also, displacement is a vector that characterizes this change. It has the additivity property. The length of the segment is the module of displacement, in the International System of Units (SI) it is measured in meters.
You can define displacement as a change in the radius vector of a point: .
The displacement modulus coincides with the distance traveled if and only if the direction of the velocity does not change during the movement. In this case, the trajectory will be a straight line segment. In any other case, for example, with curvilinear motion, it follows from the triangle inequality that the path is strictly longer.
The instantaneous speed of a point is defined as the limit of the ratio of displacement to a small period of time for which it is completed. More strictly:
See Wikipedia………………………………………………..
Question
Speed, average speed, instantaneous speed, kinematic equation for uniform rectilinear motion.
Answer
Velocity (often denoted from English velocity or French vitesse) is a vector physical quantity that characterizes the speed of movement and the direction of movement of a material point relative to the selected reference system; by definition, is equal to the derivative of the radius vector of a point with respect to time. The same word also refers to a scalar quantity - either the module of the velocity vector, or the algebraic velocity of the point, i.e. the projection of this vector onto the tangent to the trajectory of the point
Average speed - in kinematics, some average characteristic of the speed of a moving body (or material point). There are two main definitions of average speed, corresponding to the consideration of speed as a scalar or vector quantity: the average ground speed (scalar value) and the average speed over displacement (vector value). In the absence of further specifications, the average speed is usually understood as the average ground speed.
You can also enter the average speed over the movement, which will be a vector equal to the ratio of the movement to the time it took
The speed of uniform rectilinear motion of a body is a value equal to the ratio of its displacement to the time interval during which this displacement occurred.
Instantaneous speed - Instantaneous speed is the ratio of a change in the coordinate of a point to the time interval during which this change occurred, with a time interval tending to zero.
The geometric meaning of the instantaneous speed is the slope coefficient of the tangent to the graph of the law of motion.
Thus, we "attached" the value of the instantaneous speed to a specific point in time - we set the value of the speed at a given point in time, at a given point in space. Thus, we have the opportunity to consider the speed of the body as a function of time, or a function of coordinates.
Acceleration, average acceleration instantaneous acceleration, normal acceleration, tangential acceleration, kinematic equation for equally variable motion.
Answer
Question
Free fall of bodies. Acceleration of gravity.
Answer
free fall is the movement that a body would make only under the influence of gravity without taking into account air resistance. When a body falls freely from a small height h from the Earth's surface (h ≪ Rz, where Rz is the radius of the Earth), it moves with a constant acceleration g directed vertically downwards.
The acceleration g is called the free fall acceleration. It is the same for all bodies and depends only on the height above sea level and on the geographical latitude. If at the moment of the beginning of the time reference (t0 = 0) the body had a speed v0, then after an arbitrary time interval ∆t = t - t0 the free fall speed of the body will be: v = v0 + g t.
The path h traveled by the body in free fall by the time t:
The modulus of the body's velocity after passing the path h in free fall is found from the formula:
Because vk2-v02=2 g h, then
Duration ∆t of free fall without initial velocity (v0 = 0) from height h:
Example 1. A body falls vertically down from a height of 20 m without initial velocity. Define:
1) the path h traveled by the body during the last second of the fall,
2) the average rate of fall vav,
3) average speed on the second half of the way vav2.
Question
The main provisions of the molecular - kinematic theory.
Answer
Question
The concept of a molecule, atomic mass unit, relative molecular mass of atoms and molecules (Mr), amount of substance, avogadro constant, molar mass.
Answer
Question
Ideal gas. Basic equations of the molecular-kinetic theory of an ideal gas.
Answer
Equation of state of an ideal gas (Mendeleev-Clapeyron equation).
Question
Isothermal, isochoric and isobaric processes.
Answer
Question
Electric charge and its properties.
Answer
Question
Coulomb's law.
Question
Electric field. Electric field strength.
Answer
Question
The work of the field forces when moving the charge. Potential and potential difference.
Answer
Question
The laws of geometric optics, the absolute refractive index of light. Relative refractive index of light.
Answer
Question
Thin lenses, thin lens formula.
Answer
A lens is a vitreous body bounded by one or two spherical surfaces.
Material point??
Valentine
The standard definition of a material point in mechanics is a model of an object, the dimensions of which can be neglected when solving a problem. However, it can be more clearly stated as follows: a material point is a model of a mechanical system that has only translational, but not internal, degrees of freedom. This automatically means that the material point is incapable of deformation and rotation. Mechanical energy can be stored in a material point only in the form of kinetic energy of translational motion or potential energy of interaction with the field, but not in the form of rotational or deformation energy. In other words, a material point is the simplest mechanical system with the minimum possible number of degrees of freedom. A material point can have mass, charge, speed, momentum, energy.
The accuracy of this definition can be seen from the following 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 can be considered a material point. However, this is not so: vibrations and rotations of a molecule are an important reservoir of the "internal energy" of the molecule, the "capacity" of which is determined by the size of the molecule.
Material point
Material point(particle) - the simplest physical model in mechanics - an ideal body, the dimensions of which are equal to zero, one can also consider the dimensions of the body to be infinitely small compared to other dimensions or distances within the assumptions of the problem under study. The position of a material point in space is defined as the position of a geometric point.
In practice, a material point is understood as a body with mass, the size and shape of which can be neglected when solving this problem.
With a rectilinear motion of a body, one coordinate axis is sufficient to determine its position.
Peculiarities
The mass, position and speed of a material point at any particular moment of time completely determine its behavior and physical properties.
Consequences
Mechanical energy can be stored by a material point only in the form of the kinetic energy of its movement in space, and (or) the potential energy of interaction with the field. This automatically means that a material point is incapable of deformation (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 with the center, is extremely widely used in many branches of mechanics.
Restrictions
The limitations of the application 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 can be considered a material point. However, this is not always the case: vibrations and rotations of a molecule are an important reservoir of the "internal energy" of the molecule, the "capacity" of which is determined by the size of the molecule, its structure and chemical properties. In a good approximation, a monatomic molecule (inert gases, metal vapors, etc.) can sometimes be considered as a material point, but even in such molecules at a sufficiently high temperature, excitation of electron shells is observed due to molecular collisions, followed by emission.
Notes
Wikimedia Foundation. 2010 .
- mechanical movement
- Absolutely rigid body
See what "Material point" is in other dictionaries:
MATERIAL POINT is a point with mass. In mechanics, the concept of a material point is used in cases where the dimensions and shape of a body do not play a role in studying its motion, but only the mass is important. Almost any body can be considered as a material point, if ... ... Big Encyclopedic Dictionary
MATERIAL POINT- a concept introduced in mechanics to designate an object, which is considered as a point having a mass. The position of M. t. in the right is defined as the position of the geom. points, which greatly simplifies the solution of problems in mechanics. In practice, the body can be considered ... ... Physical Encyclopedia
material point- A point with mass. [Collection of recommended terms. Issue 102. Theoretical Mechanics. USSR Academy of Sciences. Committee of Scientific and Technical Terminology. 1984] Topics theoretical mechanics EN particle DE materialle Punkt FR point matériel … Technical Translator's Handbook
MATERIAL POINT Modern Encyclopedia
MATERIAL POINT- In mechanics: an infinitely small body. Dictionary of foreign words included in the Russian language. Chudinov A.N., 1910 ... Dictionary of foreign words of the Russian language
Material point- MATERIAL POINT, a concept introduced in mechanics to designate a body, the size and shape of which can be neglected. The position of a material point in space is defined as the position of a geometric point. The body can be considered material ... ... Illustrated Encyclopedic Dictionary
material point- a concept introduced in mechanics for an object of infinitesimal size, having a mass. The position of a material point in space is defined as the position of a geometric point, which simplifies the solution of problems in mechanics. Almost any body can ... ... encyclopedic Dictionary
Material point- geometric point with mass; material point is an abstract image of a material body that has mass and does not have dimensions ... Beginnings of modern natural science
material point- materialusis taškas statusas T sritis fizika atitikmenys: angl. mass point; material point vok. Massenpunkt, m; materieller Punkt, m rus. material point, f; point mass, fpranc. point mass, m; point matériel, m … Fizikos terminų žodynas
material point- A point with a mass ... Polytechnic terminological explanatory dictionary
Books
- A set of tables. Physics. Grade 9 (20 tables), . Educational album of 20 sheets. Material point. moving body coordinates. Acceleration. Newton's laws. The law of universal gravitation. Rectilinear and curvilinear motion. Body movement along...
From the seventh grade physics course, we remember that the mechanical motion of a body is its movement in time relative to other bodies. Based on such information, we can assume the necessary set of tools for calculating the movement of the body.
First, we need something in relation to which we will make our calculations. Next, we need to agree on how we will determine the position of the body relative to this "something". And finally, you will need to fix the time somehow. Thus, in order to calculate where the body will be at a particular moment, we need a frame of reference.
Frame of reference in physics
In physics, a reference system is a set of a reference body, a coordinate system associated with a reference body, and a clock or other device for measuring time. At the same time, one should always remember that any frame of reference is conditional and relative. It is always possible to adopt another frame of reference, relative to which any movement will have completely different characteristics.
Relativity is generally an important aspect that should be taken into account in almost any calculation in physics. For example, in many cases we are far from being able to determine the exact coordinates of a moving body at any time.
In particular, we cannot place observers with clocks every hundred meters along the railway line from Moscow to Vladivostok. In this case, we calculate the speed and location of the body approximately for some period of time.
We do not care about the accuracy of up to one meter when determining the location of a train on a route of several hundred or thousands of kilometers. For this, there are approximations in physics. One of such approximations is the concept of "material point".
Material point in physics
A material point in physics denotes a body, in cases where its size and shape can be neglected. It is assumed that the material point has the mass of the original body.
For example, when calculating the time it will take an airplane to fly from Novosibirsk to Novopolotsk, we do not care about the size and shape of the aircraft. It is enough to know what speed it develops and the distance between cities. In the case when we need to calculate the wind resistance at a certain height and at a certain speed, then we can’t do without an exact knowledge of the shape and dimensions of the same aircraft.
Almost any body can be considered a material point, either when the distance covered by the body is large in comparison with its size, or when all points of the body move in the same way. For example, a car that traveled a few meters from the store to the intersection is quite comparable to this distance. But even in such a situation, it can be considered a material point, because all parts of the car moved the same way and at the same distance.
But in the case when we need to place the same car in the garage, it can no longer be considered a material point. You have to take into account its size and shape. These are also examples when it is necessary to take into account relativity, that is, with respect to what we make specific calculations.
Definition
A material point is a macroscopic body whose dimensions, shape, rotation and internal structure can be neglected when describing its motion.
The question of whether a given body can be considered as a material point does not depend on the size of this body, but on the conditions of the problem being solved. For example, the radius of the Earth is much less than the distance from the Earth to the Sun, and its orbital motion can be well described as the motion of a material point with a mass equal to the mass of the Earth and located in its center. However, when considering the daily motion of the Earth around its own axis, replacing it with a material point does not make sense. The applicability of the material point model to a specific body depends not so much on the size of the body itself, but on the conditions of its motion. In particular, in accordance with the theorem on the motion of the center of mass of a system during translational motion, any rigid body can be considered a material point, the position of which coincides with the center of mass of the body.
The mass, position, speed and some other physical properties of a material point at any particular moment of time completely determine its behavior.
The position of a material point in space is defined as the position of a geometric point. In classical mechanics, the mass of a material point is assumed to be constant in time and independent of any features of its motion and interaction with other bodies. In the axiomatic approach to the construction of classical mechanics, the following is accepted as one of the axioms:
Axiom
A material point is a geometric point that is associated with a scalar called mass: $(r,m)$, where $r$ is a vector in Euclidean space related to some Cartesian coordinate system. The mass is assumed to be constant, independent of either the position of the point in space or time.
Mechanical energy can be stored by a material point only in the form of the kinetic energy of its movement in space and (or) the potential energy of interaction with the field. This automatically means that a material point is incapable of deformation (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 that set the direction of the line connecting this point with the center, is extremely widely used in many branches of mechanics.
The method of studying the laws of motion of real bodies by studying the motion of an ideal model - a material point - is the main one in mechanics. Any macroscopic body can be represented as a set of interacting material points g, with masses equal to the masses of its parts. The study of the motion of these parts is reduced to the study of the motion of material points.
The limitations of the application 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 can be considered a material point. However, this is not always the case: vibrations and rotations of a molecule are an important reservoir of the "internal energy" of the molecule, the "capacity" of which is determined by the size of the molecule, its structure and chemical properties. In a good approximation, a monatomic molecule (inert gases, metal vapors, etc.) can sometimes be considered as a material point, but even in such molecules at a sufficiently high temperature, excitation of electron shells due to molecular collisions is observed, followed by emission.
Exercise 1
a) a car entering the garage;
b) a car on the Voronezh - Rostov highway?
a) a car entering the garage cannot be taken as a material point, since under these conditions the dimensions of the car are significant;
b) a car on the Voronezh-Rostov highway can be taken as a material point, since the dimensions of the car are much smaller than the distance between cities.
Can it be taken as a material point:
a) a boy who walks 1 km on his way home from school;
b) a boy doing exercises.
a) When a boy, returning from school, walks a distance of 1 km to the house, then the boy in this movement can be considered as a material point, because his size is small compared to the distance he walks.
b) when the same boy does morning exercises, then he cannot be considered a material point.
