Table of forces in nature. Open lesson in physics. Theme: "Forces in nature". Inertial frames of reference

Sections: Physics

aim The lesson is to expand the program material on the topic: “Forces in nature” and improve practical skills and abilities in solving problems.

Lesson objectives:

reinforce the learned material,
to form students' ideas about forces in general and about each force separately,
correctly apply formulas and correctly build drawings when solving problems.

The lesson is accompanied by a multimedia presentation.

By force called a vector quantity, which is the cause of any movement as a consequence of the interactions of bodies. Interactions are contact, causing deformation, and non-contact. Deformation is a change in the shape of a body or its individual parts as a result of interaction.

In the International System of Units (SI), the unit of force is called newton (H). 1 N is equal to the force that imparts an acceleration of 1 m / s 2 to a reference body with a mass of 1 kg in the direction of the force. A device for measuring force is a dynamometer.

The force acting on a body depends on:

The magnitude of the applied force;
Points of application of force;
Directions of force.

By their nature, forces are gravitational, electromagnetic, weak and strong interactions at the field level. Gravitational forces include the force of gravity, the weight of a body, and the force of gravity. Electromagnetic forces include the force of elasticity and the force of friction. Interactions at the field level include such forces as: the Coulomb force, the Ampère force, the Lorentz force.

Consider the proposed forces.

Gravity force.

The force of gravity is determined from the law of universal gravitation and arises on the basis of the gravitational interactions of bodies, since any body with mass has a gravitational field. Two bodies interact with forces equal in magnitude and oppositely directed, directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

G = 6.67. 10 -11 - gravitational constant, determined by Cavendish.

One of the manifestations of the force of universal gravitation is the force of gravity, and the acceleration of free fall can be determined by the formula:

Where: M is the mass of the Earth, R z is the radius of the Earth.

Task: Determine the force with which two ships weighing 10 7 kg each are attracted to each other, located at a distance of 500 m from each other.

What does the force of gravity depend on?
How is the formula for the gravitational force acting at a height h from the Earth's surface?
How was the gravitational constant measured?

Gravity.

The force with which the Earth attracts all bodies to itself is called gravity. Denoted - F strand, attached to the center of gravity, directed along the radius to the center of the Earth, determined by the formula F strand = mg.

Where: m - body weight; g - free fall acceleration (g \u003d 9.8 m / s 2).

Problem: The force of gravity on the surface of the Earth is 10N. What will it be equal to at a height equal to the radius of the Earth (6.10 6 m)?

In what units is the coefficient g measured?
We know that the earth is not a sphere. It is flattened at the poles. Will the gravity of the same body be the same at the pole and the equator?
How to determine the center of gravity of a body of regular and irregular geometric shapes?

Body weight.

The force with which a body acts on a horizontal support or vertical suspension, due to gravity, is called weight. Designated - P, attached to a support or suspension under the center of gravity, directed downwards.

If the body is at rest, then it can be argued that the weight is equal to the force of gravity and is determined by the formula P = mg.

If the body moves with acceleration upwards, then the body experiences an overload. Weight is determined by the formula P \u003d m (g + a).

Body weight is approximately twice the modulus of gravity (double overload).

If the body moves with downward acceleration, then the body may experience weightlessness in the first seconds of movement. Weight is determined by the formula P \u003d m (g - a).

A task: an 80 kg elevator moves:

Evenly;

rises with an acceleration of 4.9 m / s 2 up;
descends with the same acceleration.
determine the weight of the lift in all three cases.

How is weight different from gravity?
How to find the point of application of weight?
What is overload and weightlessness?

Friction force.

The force arising from the movement of one body on the surface of another, directed in the direction opposite to the movement, is called the friction force.

The point of application of the friction force under the center of gravity, in the direction opposite to the movement along the contacting surfaces. The friction force is divided into the static friction force, the rolling friction force, and the sliding friction force. The static friction force is the force that prevents the movement of one body on the surface of another. When walking, the static friction force acting on the sole imparts acceleration to the person. When sliding, the bonds between the atoms of initially motionless bodies are broken, the friction decreases. The force of sliding friction depends on the relative velocity of the contacting bodies. Rolling friction is many times less than sliding friction.

The friction force is determined by the formula:

Where: µ is the coefficient of friction, a dimensionless value, depends on the nature of the surface treatment and on the combination of materials of the contacting bodies (the force of attraction of individual atoms various substances essentially depend on their electrical properties);

N - support reaction force - this is the elastic force that occurs in the surface under the action of the weight of the body.

For a horizontal surface: F tr = µmg

When driving solid body viscous friction occurs in a liquid or gas. The force of viscous friction is much less than the force of dry friction. It is also directed in the direction opposite to the relative velocity of the body. With viscous friction, there is no static friction. The force of viscous friction strongly depends on the speed of the body.

Task: A dog sled begins to pull a 100 kg sled standing on the snow with a constant force of 149 N. How long will it take the sledge to cover the first 200m of the path if the coefficient of sliding friction of the runners on the snow is 0.05?

What is the condition for friction?
What does the force of sliding friction depend on?
When is friction “useful” and when is it “harmful”?

Elastic force.

When the body is deformed, a force arises that seeks to restore the former dimensions and shape of the body. It is called the force of elasticity.

The simplest type of deformation is tensile or compressive deformation.

At small deformations (|x|<< l) сила упругости пропорциональна деформации тела и направлена в сторону, противоположную направлению перемещения частиц тела при деформации: F упр =kх

This ratio expresses the experimentally established Hooke's law: the elastic force is directly proportional to the change in body length.

Where: k is the stiffness coefficient of the body, measured in newtons per meter (N/m). The stiffness coefficient depends on the shape and dimensions of the body, as well as on the material.

In physics, Hooke's law for tensile or compressive deformation is usually written in a different form:

Where: - relative deformation; E - Young's modulus, which depends only on the properties of the material and does not depend on the size and shape of the body. For different materials, Young's modulus varies widely. For steel, for example, E2 10 11 N/m 2 , and for rubber E2 10 6 N/m 2 ; - mechanical stress.

At bending deformation F control = - mg and F control = - Kx.

Therefore, we can find the stiffness coefficient:

In engineering, helical springs are often used. When springs are stretched or compressed, elastic forces arise, which also obey Hooke's law, and torsion and bending deformations occur.

Task: The spring of a children's pistol was compressed by 3 cm. Determine the elastic force that arose in it if the spring stiffness is 700 N/m.

What determines the rigidity of bodies?
Explain the cause of the elastic force?
What determines the magnitude of the elastic force?

4. The resultant force.

A resultant force is a force that replaces the actions of several forces. This force is applied when solving problems using several forces.

The force of gravity and the reaction force of the support act on the body. The resultant force, in this case, is found according to the parallelogram rule and is determined by the formula

Based on the definition of the resultant, one can interpret Newton's second law as: the resultant force is equal to the product of the body's acceleration and its mass.

The resultant of two forces acting along one straight line in one direction is equal to the sum of the modules of these forces and is directed in the direction of the action of these forces. If the forces act along one straight line, but in different directions, then the resultant force is equal to the difference in the modules of the acting forces and is directed towards the action of a larger force.

Task: an inclined plane forming an angle of 30 o has a length of 25 m. the body, moving with uniform acceleration, slid off this plane in 2s. Determine the coefficient of friction.

The power of Archimedes.

The Archimedes force is a buoyant force that occurs in a liquid or gas and acts opposite to the force of gravity.

Archimedes' principle: A body immersed in a liquid or gas experiences a buoyant force equal to the weight of the displaced liquid.

Where: is the density of the liquid or gas; V is the volume of the submerged part of the body; g is the free fall acceleration.

Task: A cast-iron ball with a volume of 1 dm 3 was lowered into a liquid. Its weight has decreased by 8.9N. What liquid is the ball in?

What are the conditions for floating bodies?
Does the Archimedes force depend on the density of a body immersed in a liquid?
How is the force of Archimedes directed?

Centrifugal force.

Centrifugal force arises when moving in a circle and is directed along the radius from the center.

Where: v – linear speed; r is the radius of the circle.

Coulomb strength.

In Newtonian mechanics, the concept of gravitational mass is used, similarly, in electrodynamics, the concept of electric charge is primary. Electric charge is a physical quantity that characterizes the property of particles or bodies to enter into electromagnetic force interactions. The charges interact with the Coulomb force.

Where: q 1 and q 2 - interacting charges, measured in C (Coulomb);

r is the distance between charges; k is the coefficient of proportionality.

k=9 . 10 9 (H . m 2) / Cl 2

Often it is written in the form: , where is an electric constant equal to 8.85 . 10 12 C 2 /(N . m 2).

Interaction forces obey Newton's third law: F 1 = - F 2 . They are repulsive forces with the same signs of charges and attractive forces with different signs.

If a charged body interacts simultaneously with several charged bodies, then the resulting force acting on this body is equal to the vector sum of the forces acting on this body from all other charged bodies.

Task: The force of interaction of two identical point charges located at a distance of 0.5m is 3.6N. Find the values of these charges?

Why are both rubbing bodies charged when electrified by friction?
Does the mass of a body remain unchanged when it is electrified?
What is the physical meaning of the proportionality coefficient in Coulomb's law?

Ampere power.

An ampere force acts on a current-carrying conductor in a magnetic field.

Where: I - current strength in the conductor; B - magnetic induction; l is the length of the conductor; is the angle between the direction of the conductor and the direction of the magnetic induction vector.

The direction of this force can be determined by the left hand rule.

If the left hand should be positioned so that the lines of magnetic induction enter the palm, the outstretched four fingers are directed along the action of the current, then the bent thumb indicates the direction of the Ampère force.

Task: determine the direction of the current in a conductor in a magnetic field, if the force acting on the conductor has a direction

Under what conditions does the ampere force arise?
How to determine the direction of the Ampere force?
How to determine the direction of the lines of magnetic induction?

Lorentz force.

The force with which an electromagnetic field acts on any charged body in it is called the Lorentz force.

Where: q is the amount of charge; v is the velocity of the charged particle; B - magnetic induction; is the angle between the velocity and magnetic induction vectors.

The direction of the Lorentz force can be determined by the left hand rule.

Task: in a uniform magnetic field, the induction of which is equal to 2 T, an electron moves at a speed of 10 5 m/s perpendicular to the lines of magnetic induction. Calculate the force acting on the electron.

What is the Lorentz force?
What are the conditions for the existence of the Lorentz force?
How to determine the direction of the Lorentz force?

At the end of the lesson, students are given the opportunity to complete the table.

The name of the force	Formula	Picture	Application point	Direction of action
gravity
Gravity
The weight
Friction force
Elastic force
Strength of Archimedes
resultant force
Centrifugal force
Pendant Force
Amp power
Lorentz force

Literature:

M.Yu.Demidova, I.I.Nurminsky “USE 2009”
I.V. Krivchenko "Physics - 7"
V.A. Kasyanov “Physics. Profile Level”

Strength- a measure of the mechanical interaction of bodies. Force is the cause of a change in the speed of a body or the occurrence of deformations in it (a change in shape or volume). Force is a vector quantity characterized by its modulus (magnitude), direction and point of application of the force. The line of action of the force is a straight line passing through the point of application of the force and continuing the direction of the force vector. The SI unit of force is Newton [N]. All forces in nature are based on four types of fundamental interactions:

electromagnetic forces acting between electrically charged bodies,
gravitational forces acting between massive objects,
strong nuclear force, acting on scales of the order of the size of an atomic nucleus and less (responsible for the connection between quarks in hadrons and for the attraction between nucleons in nuclei).
weak nuclear interaction, which manifests itself at distances much smaller than the size of the atomic nucleus.

The intensity of the strong and weak interactions is measured in units of energy (electron volts), and not in units of force, and therefore the application of the term "force" to them is arbitrary. The action of force can take place both in direct contact (friction, pressure on each other in direct contact), and through the fields created by the bodies (gravitational field, electromagnetic field). An interesting and informative site http://mistermigell.ru for you.
From the point of view of the action of forces on the system, consider:

internal forces - forces of interaction between points (bodies) of a given system;
external forces - forces acting on points (bodies) of a given system from points (bodies) that do not belong to this system. External forces are called loads.

Forces can be divided into:

reactive forces − coupling reactions. If the movement of a body in space is limited by other bodies (bonds, supports), the forces with which these bodies act on a given body are called connection (support) reactions.
active forces - forces that characterize the action of other bodies on a given one and change its kinematic state. Active forces, depending on the type of contact, are divided into
volumetric - forces acting on each particle of the body, for example, the weight of the body;
surface - forces acting on a part of the body and characterizing the direct contact of the bodies. Surface forces are:
concentrated - acting on sites that are small compared to the body, for example, the pressure of a wheel on the road;
distributed - acting on sites that are not small compared to the body, for example, the pressure of a tractor caterpillar on the road.

The most famous forces:
elastic forces- the forces arising from the deformation of the body and opposing this deformation, is of an electromagnetic nature, being a manifestation of intermolecular interaction. The elastic force vector is directed opposite to the displacement, perpendicular to the surface. For example, if you compress an elastic band, after removing the load, it will restore its shape under the action of an elastic force.
Friction forces- the force arising from the relative motion of solids and opposing this motion are of an electromagnetic nature, being a macroscopic manifestation of intermolecular interaction. The friction force vector is directed opposite to the velocity vector. For example, the force of friction occurs when a sled slides on snow, between the soles of the feet and the ground.
Environmental resistance forces- the forces arising from the motion of a solid body in a liquid or gaseous medium are of an electromagnetic nature, being a manifestation of intermolecular interaction. The resistance force vector is directed opposite to the velocity vector. For example, when an aircraft is moving in the air.
Surface tension forces− the forces arising on the surface of the phase separation are electromagnetic in nature, being a manifestation of intermolecular interaction. The tension force is directed tangentially to the interface. For example, a coin can lie on the surface of a liquid, insects run on water.
The force of gravity- the force with which any bodies of the Universe attract each other, it is directly proportional to the product of the masses of these bodies and inversely proportional to the square of the distance between them. For example, the Earth is attracted to the Sun, and, at the same time, the Earth is attracted to the Moon and the Sun.
Gravity is the force acting on the body from the side of the Earth, which imparts to it the acceleration of free fall. Gravity is the sum of the forces of gravitational attraction and the centrifugal force of the Earth's rotation. For example, under the influence of gravity of a body, the Earth falls.
inertia force− fictitious force (not a measure of mechanical interaction) introduced when considering relative motion in non-inertial frames of reference (moving with acceleration) in order to fulfill Newton's second law in them. In the frame of reference associated with a uniformly accelerated body, the force of inertia is directed opposite to the acceleration. From the total force of inertia, for convenience, the centrifugal force directed from the axis of rotation of the body, and the Coriolis force, which arises when the body moves relative to the rotating frame of reference, can be distinguished for convenience.
There are other forces as well.

Denis, 6th grade, HFML % 27

There are many different types of forces in nature: gravitation, gravity, Lorentz, Ampère, interactions of fixed charges, etc., but all of them ultimately come down to a small number of fundamental (basic) interactions. Modern physics believes that there are only four types of forces or four types of interactions in nature:

1) gravitational interaction (carried out through gravitational fields);

2) electromagnetic interaction (carried out through electromagnetic fields);

3) nuclear (or strong) (ensures the connection of particles in the nucleus);

4) weak (responsible for the processes of decay of elementary particles).

Within the framework of classical mechanics, one deals with gravitational and electromagnetic forces, as well as with elastic forces and frictional forces.

Gravitational forces(gravitational forces) are the forces of attraction that obey the law of universal gravitation. Any two bodies are attracted to each other with a force whose modulus is directly proportional to the product of their masses and inversely proportional to the square of the distance between them:

where \u003d 6.67 × 10 -11 N × m 2 / kg 2 is the gravitational constant.

Gravity- the force with which the body is attracted by the Earth. Under the influence of the force of attraction to the Earth, all bodies fall with the same acceleration relative to the Earth's surface, called the acceleration of free fall. According to Newton's second law, a force acts on any body called the force of gravity. It is attached to the center of gravity.

The weight–With silt with which the body, being attracted to the Earth, acts on a suspension or support . Unlike gravity, which is a gravitational force applied to a body, weight is an elastic force applied to a support or suspension. Gravity is equal to weight only when the support or suspension is motionless relative to the Earth. The modulus of the weight can be either greater or less than the force of gravity. In the case of an accelerated movement of a support (for example, an elevator carrying a load), the equation of motion (taking into account the fact that the reaction force of the support is equal in magnitude to the weight, but has the opposite sign ): Þ . If the movement is up , way down: .

When a body is in free fall, its weight is zero, i.e. it is in a state weightlessness.

elastic forces arise as a result of the interaction of bodies, accompanied by their deformation. The elastic (quasi-elastic) force is proportional to the displacement of the particle from the equilibrium position and is directed towards the equilibrium position:

Friction forces arise due to the existence of forces of interaction between molecules and atoms of contacting bodies. The forces of thorns: a) arise when two moving bodies come into contact; b) act parallel to the contact surface; d) directed against the movement of the body.

Friction between the surfaces of solids in the absence of any interlayer or lubricant is called dry. Friction between a solid body and a liquid or gaseous medium, as well as between layers of such a medium is called viscous or liquid. There are three types of dry friction: static friction, sliding friction and rolling friction.

static friction force is the force acting between two bodies in contact when they are at rest. It is equal in magnitude and oppositely directed to the force that forces the body to move: ; , where m is the coefficient of friction.

The force of sliding friction arises when one body slides over the surface of another: and is directed tangentially to the rubbing surfaces in the direction opposite to the movement of a given body relative to another. The coefficient of sliding friction depends on the material of the bodies, the state of the surfaces and on the relative speed of the bodies.

When a body rolls on the surface of another, rolling friction force, which prevents the body from rolling. The rolling friction force with the same materials of the contacting bodies is always less than the sliding friction force. This is used in practice, replacing plain bearings with ball or roller bearings.

Elastic forces and friction forces are determined by the nature of the interaction between the molecules of a substance that is of electromagnetic origin, therefore, they are of electromagnetic origin by their nature. Gravitational and electromagnetic forces are fundamental - they cannot be reduced to other, simpler forces. Elastic forces and friction forces are not fundamental. Fundamental interactions are characterized by simplicity and precision of laws.

Despite the variety of forces, there are only four types of interactions: gravitational, electromagnetic, strong and weak.

Gravitational forces are noticeably manifested on a cosmic scale. One of the manifestations of gravitational forces is the free fall of bodies. The earth imparts to all bodies the same acceleration, which is called the free fall acceleration g. It varies slightly with geographic latitude. At the latitude of Moscow, it is equal to 9.8 m / s 2.

Electromagnetic forces act between particles that have electric charges. Strong and weak interactions are manifested inside atomic nuclei and in nuclear transformations.

Gravitational interaction exists between all bodies that have masses. Newton's law of universal gravitation states:

The force of mutual attraction of two bodies, which can be taken as material points, is directly proportional to the product of their masses and inversely proportional to the square of the distance between them:

Proportionality factor at called the gravitational constant. It is equal to 6.67 10 -11 N m 2 /kg 2.

If only the gravitational force from the Earth acts on the body, then it is equal to mg. This is the force of gravity G (without taking into account the rotation of the Earth). The force of gravity acts on all bodies on the Earth, regardless of their motion.

When a body moves with free fall acceleration (or even with a lower downward acceleration), the phenomenon of complete or partial weightlessness is observed.

Complete weightlessness - no pressure on the stand or suspension. Weight - the force of pressure of a body on a horizontal support or the tension force of a thread from the side of a body suspended from it, which arises in connection with the gravitational attraction of this body to the Earth.

The forces of attraction between bodies are indestructible, while the weight of a body can disappear. So, in a satellite that moves with the first cosmic speed around the Earth, there is no weight in the same way as in an elevator falling with an acceleration g.

An example of electromagnetic forces are the forces of friction and elasticity. Distinguish between sliding friction forces and rolling friction forces. The sliding friction force is much greater than the rolling friction force.

The force of friction depends in a certain interval on the applied force, which tends to move one body relative to another. By applying a force of varying magnitude, we will see that small forces cannot move the body. In this case, a compensating static friction force arises.

All known interactions and, accordingly, forces in nature are reduced to the following four types: gravitational, electromagnetic, strong, weak.

Gravitational interaction characteristic of all bodies in the Universe, manifests itself in the form of mutual attraction of all bodies in nature, regardless of the environment in which they are located, does not play a role in the microcosm of elementary particles at ordinary energies. A striking example is the attraction of the Earth. This interaction is subject to law of gravity : the force of interaction between two material points with masses m 1 and m 2 is directly proportional to the product of these masses and inversely proportional to the square of the distance between them. Mathematically, this law has the form:

where G\u003d 6.67 10 -11 N m 2 / kg 2 - gravitational constant, which determines the force of attraction between two identical bodies with masses m 1 = m 2 = 1 kg distance r= 1 m.

Electromagnetic interaction - interaction between fixed and moving electric charges. This interaction, in particular, determines the forces of intermolecular and interatomic interaction.

Interaction between two point fixed charges q 1 and q 2 obeys Coulomb's law:

where k\u003d 9 10 9 N m 2 / Kl 2 - coefficient of proportionality.

If a charge moves in a magnetic field, then the Lorentz force acts on it:

v is the charge rate, V is the magnetic induction vector.

Csiltyinteraction ensures the bonding of nucleons in the nucleus of an atom. Weak is responsible for most of the decays of elementary particles, as well as for the processes of interaction of neutrinos with matter.

In classical mechanics, we are dealing with gravitational and electromagnetic forces, which lead to the appearance of attractive forces, elastic forces, friction forces, and others.

Gravity characterizes the interaction of the body with the Earth.

Near the Earth, all bodies fall with approximately the same acceleration. g 9.8 m / s 2, which is called free fall acceleration. It follows that near the Earth, each body is affected by gravity, which is directed towards the center of the Earth and is equal to the product of the body's mass and the acceleration of free fall.

near the Earth's surface, the field is uniform ( g= const). Comparing
With
, we get that
.

Support reaction force - strength with which the support acts on the body. It is attached to the body and is perpendicular to the contact surface. If the body lies on a horizontal surface, then the support reaction force is numerically equal to the force of gravity. Let's consider 2 cases.

1. Consider fig.

Let the body rest, then two forces act on it. According to Newton's 2nd law

Let us find the projections of these forces on the y-axis and obtain that

2. Now let the body be on an inclined plane making an angle with the horizon (see fig.).

Consider the case when the body is at rest, then two forces will act on the body, the equation of motion looks similar to the first case. By writing down Newton's 2nd law in projection onto the y-axis, we get that the reaction force of the support is numerically equal to the projection of gravity onto the perpendicular to this surface

Body weight - the force with which a body acts on a support or suspension. The weight of the body is equal in absolute value to the support reaction force and is directed oppositely

Gravity and weight are often confused. This is due to the fact that in the case of a fixed support, these forces are the same in magnitude and in direction. However, we must remember that these forces are applied to different bodies: gravity is applied to the body itself, weight is applied to the suspension or support. In addition, the force of gravity is always equal to mg, regardless of whether the body is at rest or moving, the force of weight depends on the acceleration with which the support and the body are moving, and it can be either greater or less than mg, in particular, in a state of weightlessness, it turns to zero.

Elastic force. Under the action of external forces, a change in the shape of the body can occur - deformation. If, after the termination of the force, the shape of the body resumes, the deformation is called elastic. For elastic deformation, Hooke's law is valid:

x- elongation of the body along the axis X, k is the coefficient of proportionality, which is called coefficient elasticity.

In direct contact of bodies, in addition to elastic forces, forces of another type, the so-called friction forces, can arise.

Friction forces.

Friction forces are of two types:

The force of static friction.

Friction force due to the movement of bodies.

static friction force- the force with which a surface acts on a body resting on it in the direction opposite to the force applied to the body (see fig.) and equal to it in absolute value

Type 2 friction forces appear when contacting bodies or parts move relative to each other. Friction arising from the relative movement of two bodies in contact is called external. Friction between parts of the same solid body (liquid or gas) is called internal.

sliding friction force acts on the body in the process of its movement along the surface of another body and is equal to the product of the coefficient of friction  between these bodies and the support reaction force N and is directed in the direction opposite to the relative velocity of this body

F = N

Friction forces play a very important role in nature. In our daily life, friction is often useful. For example, the difficulties that pedestrians and vehicles experience during icy conditions, when the friction between the road surface and the soles of pedestrians or the wheels of vehicles is significantly reduced. If there were no friction forces, the furniture would have to be fastened to the floor, as on a ship during rolling, because at the slightest non-horizontality of the floor it would slide in the direction of the slope.

Law of conservation of momentum

A closed (isolated) system of bodies is a system whose bodies do not interact with external bodies or if the resultant of external forces equals zero.

If external forces do not act on the system of material points, that is, the system is isolated ( closed ), it follows from (3.12) that

(3.13)

We have received the fundamental law of classical physics - law of conservation of momentum: in an isolated (closed) system, the total momentum remains constant. In order for the law of conservation of momentum to be fulfilled, it is sufficient that the system is closed.

The law of conservation of momentum is a fundamental law of nature that knows no exceptions.

In the nonrelativistic case, one can introduce the notion center of mass (center of inertia) of a system of material points, which is understood as an imaginary point, the radius vector of which , is expressed in terms of the radii of the vectors of material points according to the formula:

(3.14)

Let us find the velocity of the center of mass in the given reference frame by taking the time derivative of relation (3.14)

. (3.14)

The momentum of the system is equal to the product of the mass of the system and the velocity of its center of inertia.

. (3.15)

The concept of the center of mass allows us to give the equation
another form, which is often more convenient. To do this, it suffices to take into account that the mass of the system is a constant value. Then

(3.16)

where is the sum of all external forces acting on the system. Equation (3.16) is the equation of motion of the center of inertia of the system. Theorem on the motion of the center of mass reads: the center of mass moves as a material point, the mass of which is equal to the total mass of the entire system, and the acting force is the geometric sum of all external forces acting on the system.

If the system is closed, then
. In this case, equation (3.16) becomes
, which implies V=const. The center of mass of a closed system moves in a straight line and uniformly.