All frames of reference are divided into inertial and non-inertial. The inertial frame of reference underlies Newtonian mechanics. It characterizes uniform rectilinear motion and a state of rest. A non-inertial frame of reference is associated with accelerated motion along a different trajectory. This motion is determined in relation to inertial reference systems. The non-inertial frame of reference is associated with such effects as inertial force, centrifugal force and Coriolis force.

All these processes arise as a result of movement, and not the interaction between bodies. Newton's laws often do not work in non-inertial frames of reference. In such cases to classical laws mechanics are added amendments. Forces due to non-inertial motion are taken into account in the development of technical products and mechanisms, including those with rotation. In life, we encounter them, moving in an elevator, riding a carousel, watching the weather and the flow of rivers. They are also taken into account when calculating the movement of spacecraft.

Inertial and non-inertial frames of reference

Inertial frames of reference are not always suitable for describing the motion of bodies. In physics, there are 2 types of reference systems: inertial and non-inertial reference systems. According to Newtonian mechanics, any body can be at rest or in uniform and rectilinear motion, except for cases when an external influence is exerted on the body. Such uniform motion is called inertial motion.

Inertial motion (inertial reference systems) is the basis of Newton's mechanics and the works of Galileo. If we consider the stars as fixed objects (which is actually not entirely true), then any objects moving uniformly and rectilinearly relative to them will form inertial frames of reference.

Unlike inertial frames of reference, a non-inertial frame moves relative to the specified one with a certain acceleration. At the same time, the use of Newton's laws requires additional variables, otherwise they will inadequately describe the system. In order to answer the question of which frames of reference are called non-inertial, it is worth considering an example of non-inertial motion. Such movement is the rotation of our and other planets.

Motion in non-inertial frames of reference

Copernicus was the first to show how complex motion can be if several forces are involved. Before him, it was believed that the Earth moves by itself, in accordance with Newton's laws, and therefore its movement is inertial. However, Copernicus proved that the Earth revolves around the Sun, that is, it makes an accelerated movement in relation to a conditionally immovable object, which may be a star.

So, there are different reference systems. Non-inertial are called only those where there is accelerated motion, which is determined in relation to the inertial frame.

Earth as a frame of reference

A non-inertial frame of reference, examples of which can be found almost everywhere, is typical for bodies with a complex trajectory of motion. The Earth revolves around the Sun, which creates the accelerated motion characteristic of non-inertial frames of reference. However, in everyday practice, everything that we encounter on Earth is quite consistent with Newton's postulates. The thing is that the corrections for non-inertial motion for reference systems connected with the Earth are very insignificant and do not play a big role for us. And Newton's equations for the same reason turn out to be generally valid.

Foucault pendulum

However, in some cases, amendments are necessary. For example, the world-famous Foucault pendulum in the Cathedral of St. Petersburg not only oscillates linearly, but also slowly turns. This rotation is due to the non-inertial motion of the Earth in outer space.

For the first time this became known in 1851 after the experiments of the French scientist L. Foucault. The experiment itself was carried out not in St. Petersburg, but in Paris, in a huge hall. The weight of the pendulum ball was about 30 kg, and the length of the connecting thread was as much as 67 meters.

In cases where only Newton's formulas for an inertial frame of reference are not enough to describe the motion, the so-called inertial forces are added to them.

Properties of a non-inertial frame of reference

The non-inertial frame of reference performs various movements relative to the inertial one. It can be forward movement, rotation, complex combined movements. The literature also provides such the simplest example non-inertial frame of reference, like a rapidly moving elevator. It is because of its accelerated movement that we feel like we are pressed to the floor, or, conversely, there is a feeling close to weightlessness. Newton's laws of mechanics cannot explain such a phenomenon. If you follow the famous physicist, then at any moment the same gravity will act on a person in an elevator, which means that the sensations should be the same, however, in reality everything is different. Therefore, it is necessary to add an additional force to Newton's laws, which is called the force of inertia.

inertia force

The force of inertia is real active force, although it differs in nature from the forces associated with the interaction between bodies in space. It is taken into account in the development of technical structures and devices, and plays an important role in their work. The forces of inertia are measured different ways, for example, using a spring dynamometer. Non-inertial frames of reference are not closed, since the forces of inertia are considered external. The forces of inertia are objective physical factors and do not depend on the will and opinion of the observer.

Inertial and non-inertial reference systems, examples of which can be found in physics textbooks, are the action of inertial force, centrifugal force, Coriolis force, momentum transfer from one body to another, and others.

Movement in the elevator

Non-inertial reference systems, inertia forces show themselves well during accelerated ascent or descent. If the elevator moves upward with acceleration, then the resulting inertia force tends to press the person to the floor, and when braking, the body, on the contrary, begins to seem lighter. In terms of manifestations, the force of inertia in this case is similar to the force of gravity, but it has a completely different nature. Gravity is gravity, which is associated with the interaction between bodies.

centrifugal forces

Forces in non-inertial frames of reference can also be centrifugal. It is necessary to introduce such a force for the same reason as the force of inertia. A striking example action of centrifugal forces - rotation on the carousel. While the chair tends to keep the person in its "orbit", the force of inertia causes the body to be pressed against the outer back of the chair. This confrontation is expressed in the appearance of such a phenomenon as centrifugal force.

Coriolis force

The action of this force is well known on the example of the rotation of the Earth. It can only be called a force conditionally, since it is not such. The essence of its action is that during rotation (for example, the Earth), each point of a spherical body moves in a circle, while objects detached from the Earth ideally move in a straight line (like, for example, a body freely flying in space). Since the line of latitude is a trajectory of rotation of points on the earth's surface, and has the form of a ring, any bodies that are torn off from it and initially moving along this line, moving linearly, begin to deviate more and more from it in the direction of lower latitudes.

Another option is when the body is launched in the meridional direction, but due to the rotation of the Earth, from the point of view of the earth observer, the movement of the body will no longer be strictly meridional.

The Coriolis force exerts big influence on the development of atmospheric processes. Under its influence, the water hits the eastern shore of the rivers flowing in the meridional direction more strongly, gradually eroding it, which leads to the appearance of cliffs. In the western one, on the contrary, precipitation is deposited, so it is more gentle and often flooded with water during floods. True, this is not the only reason leading to the fact that one side of the river is higher than the other, but in many cases it is dominant.

The Coriolis force also has experimental confirmation. It was obtained by the German physicist F. Reich. In the experiment, bodies fell from a height of 158 m. A total of 106 such experiments were carried out. During the fall, the bodies deviated from a rectilinear (from the point of view of an earthly observer) trajectory by approximately 30 mm.

Inertial frames of reference and the theory of relativity

Einstein's special theory of relativity was created in relation to inertial frames of reference. The so-called relativistic effects, according to this theory, should arise in the case of very high velocities of the body relative to the "stationary" observer. All formulas special theory relativity are also written for the uniform motion inherent in the inertial frame of reference. The first postulate of this theory asserts the equivalence of any inertial reference systems, i.e., the absence of special, distinguished systems is postulated.

However, this calls into question the possibility of testing relativistic effects (as well as the very fact of their presence), which led to the appearance of such phenomena as the twin paradox. Since the frames of reference associated with the rocket and the Earth are fundamentally equal, the effects of time dilation in the "Earth-rocket" pair will depend only on where the observer is located. So, for an observer on a rocket, time on Earth should go slower, and for a person on our planet, on the contrary, it should go slower on a rocket. As a result, the twin who remained on Earth will see his arriving brother younger, and the one who was in the rocket, having arrived, should see younger than the one who remained on Earth. It is clear that this is physically impossible.

This means that in order to observe relativistic effects, some special, distinguished frame of reference is needed. For example, it is assumed that we observe a relativistic increase in the lifetime of muons if they move at near-light speed relative to the Earth. This means that the Earth should (moreover, without alternative) have the properties of a priority, basic frame of reference, which contradicts the first postulate of SRT. Priority is possible only if the Earth is the center of the universe, which is consistent only with the primitive picture of the world and contradicts physics.

Non-inertial frames of reference as an unsuccessful way to explain the twin paradox

Attempts to explain the priority of the "terrestrial" reference system do not stand up to criticism. Some scientists associate this priority precisely with the factor of inertiality of one and non-inertiality of another frame of reference. In this case, the frame of reference associated with an observer on Earth is considered inertial, despite the fact that in physical science it is officially recognized as non-inertial (Detlaf, Yavorsky, course of physics, 2000). This is the first. The second is the same principle of equality of any reference systems. So if spaceship leaves the Earth with acceleration, then from the point of view of the observer on the ship itself, it is static, and the Earth, on the contrary, flies away from it with increasing speed.

It turns out that the Earth itself is a special reference frame, or the observed effects have a different (non-relativistic) explanation. It may be that the processes are related to the specifics of setting up or interpreting experiments, or to other physical mechanisms of the observed phenomena.

Conclusion

Thus, non-inertial frames of reference lead to the appearance of forces that have not found their place in the laws of Newtonian mechanics. When calculating for non-inertial systems, these forces must be taken into account, including when developing technical products.

Since ancient times, movement material bodies never ceased to excite the minds of scientists. So, for example, Aristotle himself believed that if no forces act on a body, then such a body will always be at rest.

And only after 2000 years, the Italian scientist Galileo Galilei was able to exclude the word "always" from Aristotle's formulation. Galileo realized that the body's being at rest is not the only consequence of the absence of external forces.

Then Galileo declared: a body on which no forces act will either be at rest or move uniformly in a straight line. That is, the movement with the same speed along a straight path, from the point of view of physics, is equivalent to a state of rest.

What is the state of rest?

In life, this fact is very difficult to observe, since there is always a friction force that does not allow objects and things to leave their places. But if we imagine an infinitely long, absolutely slippery and smooth skating rink on which the body stands, it becomes obvious that if we give the body an impulse, then the body will move infinitely long and in one straight line.

And in fact, only two forces act on the body: the force of gravity and the reaction force of the support. But they are located on the same straight line and directed against each other. Thus, by the principle of superposition, we have that the total force acting on such a body is zero.

However, this is the ideal case. In life, the force of friction manifests itself in almost all cases. Galileo made an important discovery by equating a state of rest and motion at a constant speed in a straight line. But that wasn't enough. It turned out that this condition is not satisfied in all cases.

Isaac Newton brought clarity to this issue by summarizing Galileo's research and thus formulating Newton's First Law.

Newton's first law: we formulate ourselves

There are two formulations of Newton's first law, the modern one and the formulation of Isaac Newton himself. In the original version, Newton's first law is somewhat inaccurate, and the modern version, in an attempt to correct this inaccuracy, turned out to be very confusing and therefore unsuccessful. Well, since the truth is always somewhere nearby, we will try to find it “nearby” and figure out what this law is.

Modern wording sounds like this: “There are such frames of reference, called inertial ones, with respect to which a material point, in the absence of external influences, retains the magnitude and direction of its velocity indefinitely”.

Inertial frames of reference

Inertial reference systems are called in which the law of inertia is fulfilled. The law of inertia is that bodies keep their speed unchanged if no other bodies act on them. It turns out very indigestible, incomprehensible and resembles a comical situation when the question: “Where is this“ here ”?” answer: “This is here”, and to the next logical question: “Where is this “here”?” answer: "It's here." Butter oil. Vicious circle.

Newton's own formulation is: “Every body continues to be held in a state of rest or uniform and rectilinear motion, until and in so far as it is forced by applied forces to change this state”.

However, this law is not always followed in practice. You can easily verify this. When a person stands without holding on to the handrails in a moving bus, and the bus brakes sharply, the person begins to move forward relative to the bus, although no visible force compels him to do so.

That is, with respect to the bus, Newton's first law in the original formulation is not fulfilled. Obviously it needs to be clarified. A refinement is the introduction of inertial frames of reference. That is, such reference systems in which Newton's first law is fulfilled. This is not entirely clear, so let's try to translate all this into human language.

Inertial and non-inertial frames of reference

The property of inertia of any body is such that as long as the body remains isolated from other bodies, it will retain its state of rest or uniform rectilinear motion. “Isolated” means not connected in any way, infinitely distant from other bodies.

In practice, this means that if, in our example, we take not a bus, but some star on the outskirts of the Galaxy as a reference frame, then Newton's first law will be absolutely exactly fulfilled for a careless passenger who does not hold on to the handrails. When the bus brakes, it will continue its uniform motion until other bodies act on it.

These reference systems, which are in no way connected with the body under consideration, and which do not affect the inertia of the body in any way, are called inertial. For such frames of reference, Newton's first law in its original formulation is absolutely valid.

That is the law can be formulated like this: in frames of reference that are absolutely not related to the body, the speed of the body in the absence of external influence remains unchanged. In this form, Newton's first law is easily understandable.

The problem is that in practice it is very difficult to consider the motion of a particular body with respect to such frames of reference. We cannot move to an infinitely distant star and from there carry out any experiments on Earth.

Therefore, the Earth is conventionally often taken as such a reference frame, although it is connected with the bodies located on it and affects the characteristics of their motion. But for many calculations, this approximation is sufficient. Therefore, examples of inertial reference systems can be considered the Earth for bodies located on it, solar system for her planets and so on.

Newton's first law is not described by any physical formula, but other concepts and definitions are derived using it. In fact, this law postulates the inertness of bodies. And thus it turns out that for inertial frames of reference the law of inertia is Newton's first law.

More examples of inertial systems and Newton's first law

So, for example, if a cart with a ball moves first on a flat surface, at a constant speed, and then hits a sandy surface, then the ball inside the cart will begin to accelerate, although no forces act on it (in fact, they do, but they sum is zero).

This happens because the frame of reference (in this case, the trolley) at the moment it hits the sandy surface becomes non-inertial, that is, it stops moving at a constant speed.

Newton's First Law makes an important distinction between inertial and non-inertial frames of reference. Also an important consequence of this law is the fact that acceleration, in a sense, is more important than the speed of the body.

Because moving at a constant speed in a straight line is the essence of being at rest. Whereas the movement with acceleration clearly indicates that either the sum of the forces applied to the body is not equal to zero, or the frame of reference in which the body is located is non-inertial, that is, it moves with acceleration.

Moreover, acceleration can be both positive (the body accelerates) and negative (the body slows down).

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

Aristotle believed that in the absence of movement, no forces act on the body. Let's try to find out which reference systems are called inertial, we will give examples of them.

Resting state

AT 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 does not allow many objects to leave their original position, to leave the state of rest.

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

Statement of Newton's 1st Law

In the modern interpretation, he explains the existence of coordinate systems, relative to which one can consider the absence of external forces acting on a material point. From Newton's point of view, reference systems are called inertial, which allow us to consider the conservation of the body's velocity over a long time.

Definitions

What frames of reference are inertial? Examples are studied in school course physics. Inertial reference systems are considered to be those with respect to which the 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 fulfilled in all cases. Analyzing examples of inertial and non-inertial frames of reference, consider a person holding onto the handrails in a moving vehicle. With a sharp braking of the car, a person automatically moves relative to the vehicle, despite the absence of an external force.

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

Types of reference systems

What reference systems are called inertial? It will become clear soon. “Give examples of inertial reference systems in which Newton's 1st law is fulfilled” - 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 idea about inertial and non-inertial frames of reference.

Inertia involves the preservation of rest or uniform rectilinear motion of the body as long as the body is in isolation. "Isolated" consider bodies that are not connected, do not interact, are removed from each other.

Consider some examples of an inertial frame of reference. Assuming a star in the galaxy as a frame of reference, rather than a moving bus, the implementation of the law of inertia for passengers holding on to the rails would 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 analyzed body, affect its inertness.

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

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

It is possible to calculate the acceleration in the inertial frame of reference if we consider the surface of the Earth as the frame of reference. In physics, there is no mathematical record of Newton's 1st law, but it is he who is the basis for the derivation of many physical definitions and terms.

Examples of inertial frames of reference

Students sometimes find it difficult to understand physical phenomena. Ninth-graders are offered the task of the following content: “What frames of reference are called inertial? Give examples of such systems. Assume that the cart with the ball initially moves on a flat surface with a constant speed. Then it moves along the sand, as a result, the ball is set 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 the sandy surface, the system ceases to be inertial, it has a constant speed. Examples of inertial and non-inertial frames of reference indicate that their transition occurs in a certain period of time.

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

Curvilinear motion

Relative to the stars and the Sun, the movement of the Earth is carried out along a curvilinear trajectory, which has the shape of an ellipse. That frame of reference, in which the center is aligned with the Sun, and the axes are directed to certain stars, will be considered inertial.

Note that any frame of reference that will move in a straight line and uniformly relative to the heliocentric frame is inertial. Curvilinear movement is carried out with some acceleration.

Given the fact that the Earth moves around its axis, the frame of reference, which is associated with its surface, relative to the heliocentric one moves with some acceleration. In such a situation, we can conclude that the frame of reference, which is connected with the Earth's surface, moves with acceleration relative to the heliocentric, 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 relative to it.

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

Relativity Galileo

All inertial frames of reference have 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 frame of reference.

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

• In such systems, they are the same, so any equation that is described by them, expressed in terms of coordinates and time, remains unchanged.
• The results of the ongoing mechanical experiments make it possible to establish whether the frame of reference will be at rest, or whether it will perform rectilinear uniform motion. Any system can conditionally be recognized as motionless if the other at the same time 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 another. It is possible to describe the same phenomenon in different systems, but their physical nature will not change.

Problem solving

First example.

Determine if it is an inertial frame of reference: a) artificial satellite Earth; b) children's attraction.

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

Second example.

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

Answer. a) In free fall, acceleration appears, so the frame of reference that is associated with the elevator will not be inertial.

b) With uniform movement of the elevator, the system is inertial.

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

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

Conclusion

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

At present, the system for determining the position of the body includes the body, the device for determining the time, as well as the coordinate system. Depending on whether the body is movable or stationary, it is possible to characterize the position of a certain object in the desired period of time.

Inertial Reference System (ISO)- a frame of reference in which the law of inertia is valid: all free bodies (that is, those on which external forces do not act or the action of these forces is compensated) move in them rectilinearly and uniformly or rest in them.

Non-inertial frame of reference- an arbitrary frame of reference, which is not inertial. Any frame of reference moving with acceleration relative to inertial is non-inertial.

Newton's first law - there are inertial frames of reference, i.e. such frames of reference in which the body moves uniformly and rectilinearly, if other bodies do not act on it. The main role of this law is to emphasize that in these frames of reference all accelerations acquired by bodies are consequences of the interactions of bodies. Further description of motion should be carried out only in inertial frames of reference.

 Newton's second law states that the cause of body acceleration is the interaction of bodies, the characteristic of which is force. This law gives the basic equation of dynamics, which makes it possible, in principle, to find the law of motion of a body if the forces acting on it are known. This law can be formulated as follows (Fig. 100):

acceleration of a point body (material point) is directly proportional to the sum of the forces acting on the body, and inversely proportional to the mass of the body:

here F− the resulting force, that is, the vector sum of all forces acting on the body. At first glance, equation (1) is another form of writing the definition of force given in the previous section. However, this is not quite true. First, Newton's law states that equation (1) includes the sum of all forces acting on the body, which is not in the definition of force. Secondly, Newton's second law unambiguously emphasizes that the force is the cause of the acceleration of the body, and not vice versa.

 Newton's third law emphasizes that the cause of acceleration is the mutual action of bodies on each other. Therefore, the forces acting on interacting bodies are characteristics of the same interaction. From this point of view, there is nothing surprising in Newton's third law (Fig. 101):

point bodies (material points) interact with forces equal in magnitude and opposite in direction and directed along the straight line connecting these bodies:

where F 12 − force acting on the first body from the second, a F 21 is the force acting on the second body from the first. Obviously, these forces are of the same nature. This law is also a generalization of numerous experimental facts. Let us note that in fact it is this law that is the basis for determining the mass of bodies given in the previous section.

The equation of motion of a material point in a non-inertial frame of reference can be represented as :

where - weight bodies, , - acceleration and speed of the body relative to the non-inertial frame of reference, - the sum of all external forces acting on the body, - portable acceleration bodies - Coriolis acceleration bodies, - the angular velocity of the rotational motion of the non-inertial frame of reference around the instantaneous axis passing through the origin, - the speed of the origin of the non-inertial frame of reference relative to any inertial frame of reference.

This equation can be written in the usual form Newton's second law, if you enter inertia forces:

In non-inertial frames of reference, inertial forces arise. The appearance of these forces is a sign of non-inertial reference system.

The first law of mechanics, or the law of inertia ( inertia- this is the property of bodies to maintain their speed in the absence of the action of other bodies on it ), as it is often called, was established by Galileo. But Newton gave a strict formulation of this law and included it among the fundamental laws of mechanics. The law of inertia refers to the simplest case of motion - the motion of a body that is not affected by other bodies. Such bodies are called free bodies.

It is impossible to answer the question of how free bodies move without referring to experience. However, it is impossible to set up a single experiment that would show in its pure form how a body that does not interact with anything moves, since there are no such bodies. How to be?

There is only one way out. It is necessary to create conditions for the body under which the influence of external influences can be made smaller and smaller, and observe what this leads to. It is possible, for example, to observe the movement of a smooth stone on a horizontal surface after a certain speed has been imparted to it. (A stone's attraction to the ground is balanced by the action of the surface on which it rests, and only friction affects its speed.) It is easy to find, however, that the smoother the surface, the slower the stone's speed will decrease. On smooth ice, the stone slides for a very long time, without noticeably changing speed. Friction can be reduced to a minimum by using an air cushion - jets of air that support the body above a solid surface along which movement occurs. This principle is used in water transport (hovercraft). Based on such observations, we can conclude that if the surface were perfectly smooth, then in the absence of air resistance (in vacuum), the stone would not change its speed at all. Galileo first came to this conclusion.

On the other hand, it is easy to see that when the speed of a body changes, the influence of other bodies on it is always detected. From this it can be concluded that a body far enough away from other bodies and for this reason not interacting with them moves at a constant speed.

Motion is relative, therefore it makes sense to speak only about the motion of a body with respect to a frame of reference associated with another body. The question immediately arises: will a free body move at a constant speed with respect to any other body? The answer, of course, is no. So, if in relation to the Earth a free body moves in a straight line and uniformly, then in relation to a rotating carousel the body will certainly not move in this way.

Observations of the movements of bodies and reflections on the nature of these movements lead us to the conclusion that free bodies move at a constant speed, at least with respect to certain bodies and their associated frames of reference. For example, in relation to the Earth. This is the main content of the law of inertia.

So Newton's first law can be formulated like this:

there are such frames of reference, relative to which the body (material point), in the absence of external influences on it (or with their mutual compensation), retains a state of rest or uniform rectilinear motion.

Inertial frame of reference

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

reference systems, in which Newton's first law is satisfied, are called inertial.

Inertial frames of reference- these are systems with respect 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.

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

How to establish that a given frame of reference is inertial? This can only be done by experience. Observations show that very a high degree accuracy, we can consider the heliocentric frame as an inertial frame of reference, in which the origin of coordinates is associated with the Sun, and the axes are directed to certain "fixed" stars. Frames of reference rigidly connected with the Earth's surface, strictly speaking, are not inertial, since the Earth moves in orbit around the Sun and at the same time rotates around its own axis. However, when describing motions that do not have a global (i.e. worldwide) scale, reference systems associated with the Earth can be considered inertial with sufficient accuracy.

Inertial reference frames are those that move uniformly and rectilinearly relative to any inertial frame of reference..

Galileo established that no mechanical experiments set up inside an inertial frame of reference, it is impossible to establish whether this frame is at rest or moves uniformly and rectilinearly. This statement is called Galileo's principle of relativity or 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, mathematical expression any law of physics has the same look in each inertial frame of reference. In the future, we will use only inertial systems (without mentioning this every time).

Frames of reference in which Newton's first law does not hold are called non-inertial and.

Such systems include any frame of reference moving with acceleration relative to the inertial frame of reference.

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

An example of a mechanical experiment in which the non-inertiality of a system connected with the Earth is manifested is Foucault pendulum. This is the name of a massive ball suspended on a sufficiently long thread and making small oscillations around the equilibrium position. If the system connected with the Earth were inertial, the plane of oscillation of the Foucault pendulum would remain unchanged relative to the Earth. In fact, the swing plane of the pendulum rotates due to the Earth's rotation, and the projection of the pendulum's trajectory onto the Earth's surface looks like a rosette (Fig. 1). Rice. 2

Literature

1. Open Physics 2.5 (http://college.ru/physics/)
2. Physics: Mechanics. Grade 10: Proc. for in-depth study of physics / M.M. Balashov, A.I. Gomonova, A.B. Dolitsky and others; Ed. G.Ya. Myakishev. – M.: Bustard, 2002. – 496 p.