What is an inertial frame of reference to physics. Non-inertial frame of reference: definition, examples

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 the simplest form of motion of matter - the 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.

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 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- This sequence of events. Event is called what happens at a given point in space in this moment 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. Geometric location the ends of the radius vector are 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 the 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. The clock may be in various points 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 the reasons differently causing change body condition.

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 rectilinear movement.

This - inertial system reference (ISO).

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.

We present to your attention a video lesson dedicated to the topic “Inertial reference systems. Newton's First Law", which is included in school course physics for 9th grade. 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 convenient 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: a large, large tractor is moving at a constant speed, 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 is a 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 located closer to the poles), then its value will be . The index shows that the acceleration is centripetal. Compared to acceleration free fall, 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 in the northern hemisphere, as a rule, the right bank is steeper and the left bank is flatter. In the rivers of the southern hemisphere it is the other way around. 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

Kikoin I.K., Kikoin A.K. Physics: Textbook for 9th grade high school. - M.: Enlightenment.
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.
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.

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

Homework

Formulate the definitions of inertial and non-inertial reference systems. Give examples of such systems.
State Newton's first law.
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?

Inertial reference frame

Inertial reference system(ISO) - a frame of reference in which Newton’s first law (law of inertia) is valid: all free bodies (that is, those on which external forces are not acting or the action of these forces is compensated) move rectilinearly and uniformly or are at rest. An equivalent formulation is the following, convenient for use in theoretical mechanics:

Properties of inertial reference systems

Any reference system moving relative to the ISO uniformly and rectilinearly is also an ISO. According to the principle of relativity, all ISOs are equal, and all laws of physics are invariant with respect to the transition from one ISO to another. This means that the manifestations of the laws of physics in them look the same, and the records of these laws have the same form in different ISOs.

The assumption of the existence of at least one IFR in an isotropic space leads to the conclusion that there is an infinite number of such systems moving relative to each other at all possible constant speeds. If ISOs exist, then space will be homogeneous and isotropic, and time will be homogeneous; according to Noether's theorem, homogeneity of space with respect to shifts will give the law of conservation of momentum, isotropy will lead to conservation of angular momentum, and homogeneity of time will lead to conservation of energy of a moving body.

If the velocities of relative motion of the ISOs realized by real bodies can take on any values, the connection between the coordinates and moments of time of any “event” in different ISOs is carried out by Galilean transformations.

Communication with real reference systems

Absolutely inertial systems are a mathematical abstraction that naturally does not exist in nature. However, there are reference systems in which the relative acceleration of bodies sufficiently distant from each other (measured by the Doppler effect) does not exceed 10 −10 m/s², for example, the International Celestial Coordinate System in combination with Barycentric dynamic time gives a system in which the relative accelerations do not exceed 1.5·10 −10 m/s² (at the 1σ level). The accuracy of experiments analyzing the arrival times of pulses from pulsars, and soon of astrometric measurements, is such that the acceleration should be measured in the near future solar system when it moves in the gravitational field of the Galaxy, which is estimated at m/s².

With varying degrees of accuracy and depending on the area of use, inertial systems can be considered reference systems associated with: Earth, Sun, stationary relative to the stars.

Geocentric inertial coordinate system

The use of the Earth as an ISO, despite its approximate nature, is widespread in navigation. The inertial coordinate system, as part of the ISO, is constructed according to the following algorithm. The center of the earth is selected as the O-origin point in accordance with its adopted model. The z axis coincides with the axis of rotation of the earth. The x and y axes are in the equatorial plane. It should be noted that such a system does not participate in the rotation of the Earth.

Notes

Properties of inertial reference systems

Any reference system that moves relative to the ISO uniformly, rectilinearly and without rotation is also an ISO. According to the principle of relativity, all ISOs are equal, and all laws of physics are invariant with respect to the transition from one ISO to another. This means that the manifestations of the laws of physics in them look the same, and the records of these laws have the same form in different ISOs.

The assumption of the existence of at least one ISO in an isotropic space leads to the conclusion that there is an infinite number of such systems moving relative to each other uniformly, rectilinearly and translationally at all possible speeds. If ISOs exist, then space will be homogeneous and isotropic, and time will be homogeneous; According to Noether's theorem, the homogeneity of space with respect to shifts will give the law of conservation of momentum, isotropy will lead to the conservation of angular momentum, and the homogeneity of time will lead to the conservation of energy of a moving body.

If the speeds of the relative motion of the ISOs realized by real bodies can take on any values, the connection between the coordinates and moments of time of any “event” in different ISOs is carried out by Galilean transformations.

Communication with real reference systems

Absolutely inertial systems are a mathematical abstraction and do not exist in nature. However, there are reference systems in which the relative acceleration of bodies sufficiently distant from each other (measured by the Doppler effect) does not exceed 10−10 m/s², for example,

What is an inertial frame of reference to physics. Non-inertial frame of reference: definition, examples

Properties of inertial reference systems

Communication with real reference systems

Geocentric inertial coordinate system

Notes

see also

See what “Inertial reference system” is in other dictionaries:

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Subtitles

Properties of inertial reference systems

Communication with real reference systems