Which reference system is called inertial physics. Inertial reference systems

Newton's first law postulates the presence of such a phenomenon as the inertia of bodies. Therefore it is also known as the Law of Inertia. Inertia - this is the phenomenon of a body maintaining its speed of movement (both in magnitude and direction) when no forces act on the body. To change the speed of movement, a certain force must be applied to the body. Naturally, the result of the action of forces of equal magnitude on different bodies will be different. Thus, bodies are said to have inertia. Inertia is the property of bodies to resist changes in their current state. The amount of inertia is characterized by body weight.

Inertial reference frame

Newton's first law states (which can be verified experimentally with varying degrees of accuracy) that inertial systems actually exist. This law of mechanics places inertial reference systems in a special, privileged position.

Frames of reference in which Newton's first law is satisfied are called inertial.

Inertial systems countdown- these are systems relative to which a material point, in the absence of external influences on it or their mutual compensation, is at rest or moves uniformly and rectilinearly.

There are an infinite number of inertial systems. The reference system associated with a train moving at a constant speed along a straight section of track is also an inertial system (approximately), like the system associated with the Earth. All inertial frames of reference form a class of systems that move relative to each other uniformly and rectilinearly. The accelerations of any body in different inertial systems are the same.

How to install what this system reference point is inertial? This can only be done through experience. Observations show that, with a very high degree of accuracy, a heliocentric system can be considered an inertial reference system, in which the origin of coordinates is associated with the Sun, and the axes are directed to certain “fixed” stars. Reference systems rigidly connected to the Earth's surface, strictly speaking, are not inertial, since the Earth moves in an orbit around the Sun and at the same time rotates around its axis. However, when describing movements that do not have a global (i.e., worldwide) scale, reference systems associated with the Earth can be considered inertial with sufficient accuracy.

Reference systems that move uniformly and rectilinearly relative to some inertial reference system are also inertial.

Galileo established that no mechanical experiments carried out inside an inertial reference system can establish whether this system is at rest or moves uniformly and rectilinearly. This statement is called Galileo's principle of relativity or the mechanical principle of relativity.

This principle was subsequently developed by A. Einstein and is one of the postulates of the special theory of relativity. Inertial frames of reference play an extremely important role in physics, since, according to Einstein’s principle of relativity, the mathematical expression of any law of physics has the same form in each inertial frame of reference. In what follows, we will use only inertial systems (without mentioning this every time).

Frames of reference in which Newton's first law is not satisfied are called non-inertial.

Such systems include any reference system moving with acceleration relative to an inertial reference system.

In Newtonian mechanics, the laws of interaction of bodies are formulated for a class of inertial reference systems.

An example of a mechanical experiment in which the non-inertiality of a system associated with the Earth is manifested is the behavior of the Foucault pendulum. This is the name of a massive ball suspended on a fairly long thread and performing small oscillations around the equilibrium position. If the system associated with the Earth were inertial, the plane of swing of the Foucault pendulum would remain unchanged relative to the Earth. In fact, the swing plane of the pendulum rotates due to the rotation of the Earth, and the projection of the pendulum’s trajectory onto the Earth’s surface has the shape of a rosette (Fig. 1).

The fact that the body tends to maintain not just any movement, but rectilinear movement, is evidenced, for example, by the following experience (Fig. 2). A ball moving rectilinearly along a flat horizontal surface, colliding with an obstacle having a curved shape, is forced to move in an arc under the influence of this obstacle. However, when the ball reaches the edge of the obstacle, it stops moving curvilinearly and starts moving in a straight line again. Summarizing the results of the above-mentioned (and similar) observations, we can conclude that if a given body is not acted upon by other bodies or their actions are mutually compensated, this body is at rest or the speed of its movement remains unchanged relative to the frame of reference, fixedly connected with the surface of the Earth.

Question #6:

We present to your attention a video lesson dedicated to the topic “Inertial reference systems. Newton's first law", which is included in the 9th grade school physics course. At the beginning of the lesson, the teacher will remind you of the importance of the chosen frame of reference. And then he will talk about the correctness and features of the chosen reference system, and also explain the term “inertia”.

In the previous lesson we talked about the importance of choosing a frame of reference. Let us remind you that the trajectory, distance traveled, and speed will depend on how we choose the CO. There are a number of other features associated with the choice of reference system, and we’ll talk about them.

Rice. 1. Dependence of the trajectory of a falling load on the choice of reference system

In seventh grade, you studied the concepts of “inertia” and “inertia.”

Inertia - This phenomenon, in which the body tends to maintain its original state. If the body was moving, then it should strive to maintain the speed of this movement. And if it was at rest, it will strive to maintain its state of rest.

Inertia - This property bodies maintain a state of motion. The property of inertia is characterized by such a quantity as mass. Weight – measure of body inertia. The heavier the body, the more difficult it is to move it or, conversely, to stop it.

Please note that these concepts are directly related to the concept of " inertial reference frame"(ISO), which will be discussed below.

Let us consider the motion of a body (or state of rest) in the case when the body is not acted upon by other bodies. The conclusion about how a body will behave in the absence of the action of other bodies was first proposed by Rene Descartes (Fig. 2) and continued in the experiments of Galileo (Fig. 3).

Rice. 2. Rene Descartes

Rice. 3. Galileo Galilei

If a body moves and other bodies do not act on it, then the movement will be maintained, it will remain rectilinear and uniform. If other bodies do not act on the body, and the body is at rest, then the state of rest will be maintained. But it is known that the state of rest is associated with a reference system: in one reference frame the body is at rest, and in the other it moves quite successfully and at an accelerated rate. The results of experiments and reasoning lead to the conclusion that not in all reference systems a body will move rectilinearly and uniformly or be at rest in the absence of the action of other bodies on it.

Consequently, to solve the main problem of mechanics, it is important to choose a reporting system where the law of inertia is still satisfied, where the reason that caused the change in the motion of the body is clear. If the body moves rectilinearly and uniformly in the absence of the action of other bodies, such a frame of reference will be preferable for us, and it will be called inertial reference system(ISO).

Aristotle's view on the cause of motion

The inertial frame of reference is comfortable model to describe the movement of a body and the reasons that cause such movement. This concept first appeared thanks to Isaac Newton (Fig. 5).

Rice. 5. Isaac Newton (1643-1727)

The ancient Greeks imagined movement completely differently. We will get acquainted with the Aristotelian point of view on motion (Fig. 6).

Rice. 6. Aristotle

According to Aristotle, there is only one inertial frame of reference - the frame of reference associated with the Earth. All other reference systems, according to Aristotle, are secondary. Accordingly, all movements can be divided into two types: 1) natural, that is, those communicated by the Earth; 2) forced, that is, everyone else.

The simplest example of natural motion is the free fall of a body to the Earth, since the Earth in this case imparts speed to the body.

Let's look at an example of forced movement. This is a horse pulling a cart situation. While the horse is exerting force, the cart is moving (Fig. 7). As soon as the horse stopped, the cart stopped too. No strength - no speed. According to Aristotle, it is force that explains the presence of speed in a body.

Rice. 7. Forced movement

Until now, some ordinary people consider Aristotle’s point of view to be fair. For example, Colonel Friedrich Kraus von Zillergut from “The Adventures of the Good Soldier Schweik during the World War” tried to illustrate the principle “No strength - no speed”: “When all the gasoline ran out,” said the colonel, “the car was forced to stop. I saw this myself yesterday. And after that they still talk about inertia, gentlemen. It doesn’t go, it stands there, it doesn’t move. No gasoline! Isn’t it funny?”

As in modern show business, where there are fans, there will always be critics. Aristotle also had his critics. They suggested that he do the following experiment: release the body, and it will fall exactly under the place where we released it. Let us give an example of criticism of Aristotle's theory, similar to the examples of his contemporaries. Imagine that a flying plane is throwing a bomb (Fig. 8). Will the bomb fall exactly under the place where we released it?

Rice. 8. Illustration for example

Of course not. But this is a natural movement - a movement that was communicated by the Earth. Then what makes this bomb move forward? Aristotle answered this way: the fact is that the natural movement that the Earth imparts is falling straight down. But when moving in the air, the bomb is carried away by its turbulence, and these turbulences seem to push the bomb forward.

What happens if the air is removed and a vacuum is created? After all, if there is no air, then, according to Aristotle, the bomb should fall exactly under the place where it was thrown. Aristotle argued that if there is no air, then such a situation is possible, but in fact there is no emptiness in nature, there is no vacuum. And if there is no vacuum, there is no problem.

And only Galileo Galilei formulated the principle of inertia in the form to which we are accustomed. The reason for the change in speed is the action of other bodies on the body. If other bodies do not act on the body or this action is compensated, then the speed of the body will not change.

The following considerations can be made regarding the inertial frame of reference. Imagine a situation when a car is moving, then the driver turns off the engine, and then the car moves by inertia (Fig. 9). But this is an incorrect statement for the simple reason that over time the car will stop as a result of friction. Therefore, in this case there will be no uniform motion - one of the conditions is missing.

Rice. 9. The speed of the car changes as a result of friction

Let's consider another case: with constant speed A large, large tractor is moving, while in front it is dragging a large load with a bucket. Such movement can be considered as rectilinear and uniform, because in this case all the forces that act on the body are compensated and balance each other (Fig. 10). This means that the frame of reference associated with this body can be considered inertial.

Rice. 10. The tractor moves evenly and in a straight line. The action of all bodies is compensated

There can be a lot of inertial reference systems. In reality, such a reference system is still idealized, since upon closer examination there are no such reference systems in the full sense. ISO is a kind of idealization that allows you to effectively simulate real physical processes.

For inertial reference systems, Galileo's formula for adding velocities is valid. We also note that all the reference systems that we talked about before can be considered inertial to some approximation.

The law dedicated to ISO was first formulated by Isaac Newton. Newton's merit lies in the fact that he was the first to scientifically show that the speed of a moving body does not change instantly, but as a result of some action over time. This fact formed the basis for the creation of the law that we call Newton’s first law.

Newton's first law : there are such reference systems in which the body moves rectilinearly and uniformly or is at rest if no forces act on the body or all forces acting on the body are compensated. Such reference systems are called inertial.

In another way, they sometimes say this: an inertial frame of reference is a system in which Newton’s laws are satisfied.

Why is the Earth a non-inertial CO? Foucault pendulum

IN large quantities problems, it is necessary to consider the motion of a body relative to the Earth, while we consider the Earth to be an inertial frame of reference. It turns out that this statement is not always true. If we consider the movement of the Earth relative to its axis or relative to the stars, then this movement occurs with some acceleration. CO, which moves with a certain acceleration, cannot be considered inertial in the full sense.

The earth rotates around its axis, which means all points lying on its surface continuously change the direction of their speed. Speed ​​- vector quantity. If its direction changes, then some acceleration appears. Therefore, the Earth cannot be a correct ISO. If we calculate this acceleration for points located on the equator (points that have maximum acceleration relative to points closer to the poles), then its value will be . The index shows that the acceleration is centripetal. In comparison with the acceleration due to gravity, acceleration can be neglected and the Earth can be considered an inertial frame of reference.

However, during long-term observations one cannot forget about the rotation of the Earth. This was convincingly shown by the French scientist Jean Bernard Leon Foucault (Fig. 11).

Rice. 11. Jean Bernard Leon Foucault (1819-1868)

Foucault pendulum(Fig. 12) - it is a massive weight suspended from a very long thread.

Rice. 12. Foucault pendulum model

If the Foucault pendulum is taken out of equilibrium, then it will describe the following trajectory other than a straight line (Fig. 13). The displacement of the pendulum is caused by the rotation of the Earth.

Rice. 13. Oscillations of the Foucault pendulum. View from above.

The rotation of the Earth is caused by a number of other interesting facts. For example, in rivers northern hemisphere, as a rule, the right bank is steeper, and the left bank is flatter. In the rivers southern hemisphere- vice versa. All this is due precisely to the rotation of the Earth and the resulting Coriolis force.

On the question of the formulation of Newton's first law

Newton's first law: if no bodies act on a body or their action is mutually balanced (compensated), then this body will be at rest or move uniformly and rectilinearly.

Let's consider a situation that will indicate to us that this formulation of Newton's first law needs to be corrected. Imagine a train with curtained windows. In such a train, the passenger cannot determine whether the train is moving or not by looking at objects outside. Let's consider two reference systems: FR associated with the passenger Volodya and FR associated with the observer on the platform Katya. The train begins to accelerate, its speed increases. What will happen to the apple that is on the table? It will roll by inertia into the opposite side. For Katya it will be obvious that the apple is moving by inertia, but for Volodya it will be incomprehensible. He does not see that the train has begun its movement, and suddenly an apple lying on the table begins to roll towards him. How can this be? After all, according to Newton's first law, the apple must remain at rest. Therefore, it is necessary to improve the definition of Newton's first law.

Rice. 14. Illustration example

Correct formulation of Newton's first law sounds like this: there are reference systems in which the body moves rectilinearly and uniformly or is at rest if no forces act on the body or all forces acting on the body are compensated.

Volodya is in a non-inertial frame of reference, and Katya is in an inertial one.

Most of the systems, real reference systems, are non-inertial. Let's consider a simple example: while sitting on a train, you put some body (for example, an apple) on the table. When the train starts moving, we will observe the following interesting picture: the apple will move, roll in the direction opposite to the movement of the train (Fig. 15). In this case, we will not be able to determine what bodies act and make the apple move. In this case the system is said to be non-inertial. But you can get out of this situation by entering inertia force.

Rice. 15. Example of non-inertial FR

Another example: when a body moves along a curved road (Fig. 16), a force arises that causes the body to deviate from the straight direction of movement. In this case we must also consider non-inertial reference frame, but, as in the previous case, we can also get out of the situation by introducing the so-called. inertia forces.

Rice. 16. Inertia forces when moving along a rounded path

Conclusion

There are an infinite number of reference systems, but most of them are those that we cannot consider as inertial reference systems. An inertial reference frame is an idealized model. By the way, with such a reference system we can accept a reference system associated with the Earth or some distant objects (for example, with stars).

Bibliography

1. Kikoin I.K., Kikoin A.K. Physics: Textbook for 9th grade high school. - M.: Enlightenment.
2. Peryshkin A.V., Gutnik E.M. Physics. 9th grade: textbook for general education. institutions / A. V. Peryshkin, E. M. Gutnik. - 14th ed., stereotype. - M.: Bustard, 2009. - 300.
3. Sokolovich Yu.A., Bogdanova G.S. Physics: A reference book with examples of problem solving. - 2nd edition, revision. - X.: Vesta: Ranok Publishing House, 2005. - 464 p.

1. Internet portal “physics.ru” ()
2. Internet portal “ens.tpu.ru” ()
3. Internet portal “prosto-o-slognom.ru” ()

Homework

1. Formulate the definitions of inertial and non-inertial reference systems. Give examples of such systems.
2. State Newton's first law.
3. In ISO the body is at rest. Determine what is the value of its speed in the ISO, which moves relative to the first reference frame with speed v?

Any reference system that moves translationally, uniformly and rectilinearly with respect to an inertial reference system is also an inertial reference system. Therefore, theoretically, any number of inertial frames of reference can exist.

In reality, the reference system is always associated with some specific body in relation to which the movement of various objects is studied. Since all real bodies move with one or another acceleration, any real reference system can be considered as an inertial reference system only with a certain degree of approximation. With a high degree of accuracy, the heliocentric system associated with the center of mass can be considered inertial solar system and with axes directed towards three distant stars. Such an inertial reference system is used mainly in problems of celestial mechanics and astronautics. To solve most technical problems, a reference system rigidly connected to the Earth can be considered inertial.

Galileo's principle of relativity

Inertial frames of reference have an important property that describes Galileo's principle of relativity:

• any mechanical phenomenon under the same initial conditions proceeds in the same way in any inertial frame of reference.

The equality of inertial reference systems established by the principle of relativity is expressed in the following:

1. the laws of mechanics in inertial frames of reference are the same. This means that the equation describing a certain law of mechanics, being expressed through the coordinates and time of any other inertial reference system, will have the same form;
2. according to the results mechanical experiments it is impossible to establish whether a given frame of reference is at rest or moves uniformly and rectilinearly. Because of this, none of them can be singled out as a predominant system, the speed of movement of which could be given an absolute meaning. Physical meaning has only the concept of the relative speed of movement of systems, so that any system can be considered conditionally motionless, and another - moving relative to it with a certain speed;
3. the equations of mechanics are unchanged with respect to coordinate transformations when moving from one inertial reference system to another, i.e. the same phenomenon can be described in two ways different systems counting outwardly differently, but physical nature the phenomenon remains unchanged.

Examples of problem solving

EXAMPLE 1

EXAMPLE 2

Ancient philosophers tried to understand the essence of movement, to identify the impact of stars and the Sun on humans. In addition, people have always tried to identify the forces that act on a material point during its movement, as well as at the moment of rest.

Aristotle believed that in the absence of movement, the body is not affected by any forces. Let's try to find out which reference systems are called inertial, and give examples of them.

State of rest

IN Everyday life it is difficult to identify such a condition. Almost all types mechanical movement the presence of outside forces is assumed. The reason is the force of friction, which prevents many objects from leaving their original position and leaving a state of rest.

Considering examples of an inertial reference system, we note that they all comply with Newton’s 1st law. Only after its discovery was it possible to explain the state of rest and indicate the forces acting on the body in this state.

Statement of Newton's 1st law

In the modern interpretation, it explains the existence of coordinate systems, in relation to which one can consider the absence of influence on a material point by external forces. From Newton's point of view, reference systems are called inertial, which allow us to consider the conservation of the speed of a body over a long time.

Definitions

Which reference systems are inertial? Examples of them are studied in the school physics course. Inertial systems are considered to be those frames of reference relative to which a material point moves at a constant speed. Newton clarified that any body can be in a similar state as long as there is no need to apply forces to it that can change such a state.

In reality, the law of inertia is not satisfied in all cases. Analyzing examples of inertial and non-inertial reference systems, consider a person holding the handrails in a moving vehicle. When a car suddenly brakes, a person automatically moves relative to the vehicle, despite the absence of external force.

It turns out that not all examples of an inertial reference system correspond to the formulation of Newton's 1st law. To clarify the law of inertia, a refined reference was introduced, in which it is impeccably fulfilled.

Types of reference systems

What reference systems are called inertial? This will soon become clear. “Give examples of inertial reference systems in which Newton’s 1st law is satisfied” - a similar task is offered to schoolchildren who have chosen physics as an exam in the ninth grade. In order to cope with the task, it is necessary to have an understanding of inertial and non-inertial reference systems.

Inertia involves maintaining rest or uniform linear motion of a body as long as the body is isolated. “Isolated” are considered bodies that are not connected, do not interact, and are distant from each other.

Let's look at some examples of inertial reference systems. If we consider the reference frame to be a star in the Galaxy, and not a moving bus, the fulfillment of the law of inertia for passengers holding on to the handrails will be flawless.

During braking this vehicle will continue uniform rectilinear motion until other bodies act on it.

What are some examples of an inertial frame of reference? They should not have a connection with the body being analyzed or affect its inertia.

It is for such systems that Newton's 1st law is satisfied. IN real life it is difficult to consider the movement of a body relative to inertial frames of reference. It is impossible to get to a distant star in order to conduct earthly experiments from it.

As conditional systems the Earth is taken as reference, despite the fact that it is connected with objects placed on it.

Acceleration in an inertial reference frame can be calculated if we consider the Earth's surface as the reference frame. In physics there is no mathematical representation of Newton's 1st law, but it is the basis for the derivation of many physical definitions and terms.

Examples of inertial reference systems

Students sometimes find it difficult to understand physical phenomena. Ninth-graders are offered a task with the following content: “Which reference systems are called inertial? Give examples of such systems." Let us assume that the cart with the ball initially moves on a flat surface at a constant speed. Then it moves along the sand, as a result the ball is put into accelerated motion, despite the fact that no other forces act on it (their total effect is zero).

The essence of what is happening can be explained by the fact that while moving along a sandy surface, the system ceases to be inertial, it has a constant speed. Examples of inertial and non-inertial reference systems indicate that their transition occurs in a certain period of time.

When a body accelerates, its acceleration has a positive value, and when braking, this indicator becomes negative.

Curvilinear movement

Relative to the stars and the Sun, the Earth's movement occurs along a curvilinear trajectory, which has the shape of an ellipse. The reference system in which the center is aligned with the Sun, and the axes are directed to certain stars, will be considered inertial.

Note that any reference system that will move rectilinearly and uniformly relative to the heliocentric system is inertial. Curvilinear movement carried out with some acceleration.

Considering the fact that the Earth moves around its axis, the reference frame that is associated with its surface, relative to the heliocentric one, moves with some acceleration. In such a situation, we can conclude that the reference frame, which is associated with the surface of the Earth, moves with acceleration relative to the heliocentric one, so it cannot be considered inertial. But the value of the acceleration of such a system is so small that in many cases it significantly affects the specifics of the mechanical phenomena considered in relation to it.

In order to solve practical problems of a technical nature, it is customary to consider the frame of reference that is rigidly connected to the surface of the Earth to be inertial.

Galileo's relativity

All inertial frames of reference have an important property, which is described by the principle of relativity. Its essence lies in the fact that any mechanical phenomenon under the same initial conditions is carried out in the same way, regardless of the chosen reference system.

The equality of ISO according to the principle of relativity is expressed in the following provisions:

• In such systems they are the same, therefore any equation that is described by them, expressed in terms of coordinates and time, remains unchanged.
• The results of the conducted mechanical experiments make it possible to establish whether the reference system will be at rest, or whether it will perform a rectilinear uniform motion. Any system can be conditionally recognized as stationary if another system moves relative to it at a certain speed.
• The equations of mechanics remain unchanged with respect to coordinate transformations in the case of transition from one system to the second. It is possible to describe the same phenomenon in different systems, but their physical nature will not change.

Problem solving

First example.

Determine whether the inertial frame of reference is: a) artificial satellite Earth; b) children's attraction.

Answer. In the first case not there is talk about the inertial reference frame, since the satellite moves in orbit under the influence of the force of gravity, therefore, the movement occurs with some acceleration.

Second example.

The reporting system is firmly connected to the elevator. In what situations can it be called inertial? If the elevator: a) falls down; b) moves uniformly upward; c) rises rapidly; d) uniformly directed downwards.

Answer. a) When free fall acceleration appears, so the reference system associated with the elevator will not be inertial.

b) When the elevator moves uniformly, the system is inertial.

c) When moving with some acceleration, the reference system is considered inertial.

d) The elevator moves slowly and has negative acceleration, so the reference frame cannot be called inertial.

Conclusion

Throughout its existence, humanity has been trying to understand the phenomena occurring in nature. Attempts to explain the relativity of motion were made by Galileo Galilei. Isaac Newton managed to derive the law of inertia, which began to be used as the main postulate when carrying out calculations in mechanics.

Currently, a body position determination system includes a body, a device for determining time, and a coordinate system. Depending on whether the body is moving or stationary, it is possible to characterize the position of a certain object in the desired period of time.

General physics course

Introduction.

Physics (Greek, from physis - nature), the science of nature, studying the simplest and at the same time the most general properties material world (patterns of natural phenomena, properties and structure of matter and the laws of its movement). The concepts of physics and its laws underlie all natural science. Physics belongs to the exact sciences and studies the quantitative laws of phenomena. Therefore, naturally, the language of physics is mathematics.

Matter can exist in two main forms: substance and field. They are interconnected.

Examples: B more – solids, liquids, plasma, molecules, atoms, elementary particles, etc.

Field– electromagnetic field (quanta (portions) of the field – photons);

gravitational field (field quanta - gravitons).

Relationship between matter and field– annihilation of an electron-positron pair.

Physics is certainly a worldview science, and knowledge of its fundamentals is necessary element any education, culture of modern man.

At the same time, physics has enormous applied significance. It is to her that the absolute majority of technical, information and communication achievements of mankind are owed.

Moreover, in recent decades physical methods research is increasingly being used in sciences that seem far from physics, such as sociology and economics.

Classical mechanics.

Mechanics is a branch of physics that studies simplest form motion of matter – movement of bodies in space and time.

Initially, the basic principles (laws) of mechanics as a science were formulated by I. Newton in the form of three laws, which received his name.

Using the vector method of description, speed can be defined as the derivative of the radius vector of a point or body , and mass acts here as a coefficient of proportionality.

1. When two bodies interact, each of them acts on the other body with a force that is equal in value but opposite in direction.

These laws come from experience. All classical mechanics are built on them. For a long time it was believed that all observable phenomena could be described by these laws. However, over time, the boundaries of human capabilities expanded, and experience showed that Newton’s laws are not always valid, and classical mechanics, as a consequence, has certain limits of applicability.

In addition, a little later we will turn to classical mechanics from a slightly different angle - based on conservation laws, which in a sense are more general laws of physics than Newton's laws.

1.2. Limits of applicability of classical mechanics.

The first limitation is related to the speeds of the objects in question. Experience has shown that Newton's laws remain valid only if , where the speed of light in vacuum ( ). At these speeds, linear scales and time intervals do not change when moving from one reference system to another. That's why space and time are absolute in classical mechanics.

So, classical mechanics describes motion with low relative speeds, i.e. This is non-relativistic physics. The limitation from high speeds is the first limitation of the application of classical Newtonian mechanics.

In addition, experience shows that the application of the laws of Newtonian mechanics is inappropriate to the description of micro-objects: molecules, atoms, nuclei, elementary particles etc. Starting with sizes

(), an adequate description of the observed phenomena is given by others

laws - quantum. They are the ones that need to be used when the characteristic quantity that describes the system and has the dimension , is comparable in order to Planck's constant. Let's say, for an electron located in an atom, we have . Then the quantity having the dimension of angular momentum is equal to: .

Any physical phenomenon is sequence of events. Event is called what happens at a given point in space at a given moment in time.

To describe events, enter space and time– categories denoting the main forms of existence of matter. Space expresses the order of existence of individual objects, and time expresses the order of change of phenomena. Space and time must be marked out. Marking is carried out by introducing reference bodies and reference (scale) bodies.

Frames of reference. Inertial reference systems.

To describe the movement of a body or the model used - a material point - can be used vector method descriptions when the position of the object of interest to us is specified using the radius vector a segment directed from the reference body to a point of interest to us, the position of which in space can change over time. The geometric locus of the ends of the radius vector is called trajectory moving point.

2.1. Coordinate systems.

Another way to describe the movement of a body is coordinate, in which a certain coordinate system is rigidly associated with the reference body.

In mechanics, and in physics in general, it is convenient to use in various tasks various systems coordinates The most commonly used are the so-called Cartesian, cylindrical and spherical coordinate systems.

1) Cartesian coordinate system: three mutually perpendicular axes are entered with specified scales along all three axes (rulers). The reference point for all axes is taken from the reference body. The limits of change for each of the coordinates from to .

The radius vector defining the position of a point is determined through its coordinates as

. (2.1)

Small volume in Cartesian system:

,

or in infinitesimal increments:

(2.2)

2) Cylindrical coordinate system: the variables chosen are the distance from the axis, the angle of rotation from the x-axis, and the height along the axis from the reference body.

3) Spherical coordinate system: enter the distance from the reference body to the point of interest and angles

rotation and , measured from the axes and , respectively.

Radius vector – function of variables

,

limits of coordinate changes:

Cartesian coordinates are related to spherical coordinates by the following relations

(2.6)

Volume element in spherical coordinates:

(2.7)

2.2. Reference system.

To construct a reference system, a coordinate system rigidly connected to the reference body must be supplemented with a clock. Clocks can be located at different points in space, so they need to be synchronized. Clock synchronization is done using signals. Let the signal propagation time from the point where the event occurred to the observation point be equal to . Then our watch should show the time at the moment the signal appears , if the clock at the point of the event at the moment of its occurrence shows the time. We will consider such clocks to be synchronized.

If the distance from the point in space where the event occurred to the observation point is , and the signal transmission speed is , then . In classical mechanics it is accepted that the speed of signal propagation . Therefore, one clock is introduced throughout the entire space.

Totality reference bodies, coordinate systems and clocks form Frame of reference(SO).

There are an infinite number of reference systems. Experience shows that the speeds are still small compared to the speed of light , linear scales and time intervals do not change when moving from one reference system to another.

In other words, in classical mechanics space and time are absolute.

If , then the scales and time intervals depend on the choice of reference data, i.e. space and time become relative concepts. This is already an area relativistic mechanics.

2.3.Inertial reference systems(ISO).

So, we are faced with the choice of a reference system in which we could solve problems of mechanics (describe the movement of bodies and establish the reasons that cause it). It turns out that not all reference systems are equal, not only in the formal description of the problem, but, what is much more important, they represent differently the reasons that cause a change in the state of the body.

The frame of reference in which the laws of mechanics are formulated most simply allows us to establish Newton's first law, which postulates the existence inertial reference systems– ISO.

First law of classical mechanics – Galileo-Newton law of inertia.

There is a reference system in which a material point, if we exclude its interaction with all other bodies, will move by inertia, i.e. maintain a state of rest or uniform linear motion.

This is an inertial reference system (IRS).

In ISO, the change in the motion of a material point (acceleration) is caused only by its interaction with other bodies, but does not depend on the properties of the reference system itself.