Inertial reference system (IRS)- a frame of reference in which the law of inertia is valid: all free bodies (that is, those that are not acted upon by external forces or the action of these forces is compensated) move in them rectilinearly and uniformly or are at rest in them.
Non-inertial reference frame- an arbitrary reference system that is not inertial. Any reference system moving with acceleration relative to an inertial one is non-inertial.
Newton's first law - there are inertial reference systems, i.e., such reference systems in which a 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 reference systems all accelerations acquired by bodies are consequences of the interactions of bodies. Further description of the motion should be carried out only in inertial reference systems.
Newton's second law states that the reason for the acceleration of a body is the interaction of bodies, the characteristic of which is force. This law gives the basic equation of dynamics, which allows, 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):
the acceleration of a point body (material point) is directly proportional to the sum of forces acting on the body, and inversely proportional to the mass of the body:
Here F− resultant 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 a body, which is not the definition of force. Secondly, Newton's second law clearly emphasizes that force is the cause of acceleration of a 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 − force acting on the second body from the first. It is obvious that 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 the definition of the mass of bodies given in the previous section.
The equation of motion of a material point in a non-inertial reference frame can be represented as :
Where - weight body, , - acceleration and speed of the body relative to a non-inertial reference frame, - the sum of all external forces acting on the body, - portable acceleration body, - Coriolis acceleration body, - the angular velocity of the rotational motion of the non-inertial reference system around the instantaneous axis passing through the origin of coordinates, - the speed of movement of the origin of the non-inertial reference system relative to any inertial reference system.
This equation can be written in the usual form Newton's second law, if you enter inertia forces:
In non-inertial reference systems, inertial forces arise. The appearance of these forces is a sign of non-inertiality of the reference system.
All reference systems are divided into inertial and non-inertial. The inertial frame of reference underlies Newtonian mechanics. It characterizes uniform linear motion and a state of rest. A non-inertial reference frame is associated with accelerated motion along a different trajectory. This motion is defined with respect to inertial reference frames. 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 interaction between bodies. Newton's laws often do not work in non-inertial frames of reference. In such cases, amendments are added to the classical laws of mechanics. Forces due to non-inertial motion are taken into account when designing technical products and mechanisms, including those where rotation is present. 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 motion of spacecraft.
Inertial and non-inertial reference systems
Inertial reference systems 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 uniform and rectilinear motion, except in cases where the body is subject to external influence. Such uniform motion is called motion by inertia.
Inertial motion (inertial frames of reference) forms the basis of Newton's mechanics and the works of Galileo. If we consider stars to be stationary 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 reference systems, a non-inertial frame moves relative to the specified one with a certain acceleration. Moreover, the use of Newton's laws requires additional variables, otherwise they will not adequately describe the system. To answer the question of which reference systems are called non-inertial, it is worth considering an example of non-inertial motion. This movement is the rotation of our and other planets.
Motion in non-inertial frames of reference
Copernicus was the first to show how complex movement can be if several forces are involved. Before him, it was believed that the Earth moves on its own, 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 undergoes accelerated motion in relation to a conditionally stationary object, which could be a star.
So there is different systems countdown. Only those where there is accelerated motion, which is determined in relation to the inertial system, are called non-inertial.
Earth as a frame of reference
A non-inertial reference system, examples of the existence of which can be found almost everywhere, is typical for bodies with a complex trajectory of motion. The Earth rotates around the Sun, which creates accelerated motion, characteristic of non-inertial reference systems. However, in everyday practice everything we encounter on Earth is completely consistent with Newton’s postulates. The thing is that corrections for non-inertial motion for reference systems associated with the Earth are very insignificant and do not play a big role for us. And for the same reason, Newton’s equations turn out to be generally valid.
Foucault pendulum
However, in some cases amendments cannot be avoided. For example, the world-famous Foucault pendulum in the St. Petersburg Cathedral not only oscillates linearly, but also rotates slowly. This rotation is due to the non-inertial motion of the Earth in outer space.
This first 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 Newton’s formulas for an inertial reference frame alone are not enough to describe motion, so-called inertial forces are added to them.
Properties of a non-inertial reference frame
The non-inertial reference system performs various movements relative to the inertial one. This can be translational movement, rotation, complex combined movements. In the literature there is also such simplest example non-inertial reference frame, like an accelerated elevator. It is because of its accelerated movement that we feel like we are being pressed to the floor, or, conversely, a sensation close to weightlessness arises. Newton's laws of mechanics cannot explain this phenomenon. If you follow the famous physicist, then at any moment the same force of gravity will act on a person in the elevator, which means 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 acting force, although it differs in nature from the forces associated with the interaction between bodies in space. It is taken into account during development technical designs and devices, and plays important role in their work. Inertia forces are measured different ways, for example, using a spring dynamometer. Non-inertial reference systems are not closed, since inertial forces are considered external. Inertial forces are objective physical factors and do not depend on the will and opinion of the observer.
Inertial and non-inertial reference systems, examples of the manifestation of which can be found in physics textbooks, are the action of inertial force, centrifugal force, Coriolis force, transfer of momentum from one body to another, and others.
Movement in the elevator
Non-inertial reference systems and inertial forces manifest themselves well during accelerated ascent or descent. If the elevator accelerates upward, then the resulting inertial force tends to press the person to the floor, and when braking, the body, on the contrary, begins to seem lighter. In terms of its 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 reference systems can also be centrifugal. It is necessary to introduce such a force for the same reason as the force of inertia. A striking example of the action of centrifugal forces is rotation on a carousel. While the chair strives 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 effect of this force is well known from the example of the rotation of the Earth. It can only be called 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 separated from the Earth ideally move in a straight line (such as, for example, a body freely flying in space). Since the line of latitude is the trajectory of the rotation of points earth's surface, and has the form of a ring, then any bodies 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 an earthly observer, the movement of the body will no longer be strictly meridional.
The Coriolis force has a great influence on the development of atmospheric processes. Under its influence, the water hits the eastern bank of rivers flowing in the meridional direction more strongly, gradually eroding it, which leads to the appearance of cliffs. On the western side, on the contrary, precipitation is deposited, so it is flatter and is often flooded with water during floods. True, this is not the only reason leading to the fact that one bank 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. When falling, 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 reference systems. The so-called relativistic effects, according to this theory, should arise in the case of very high speeds of movement of a body relative to a “stationary” observer. All formulas of the special theory of relativity are also written for uniform motion characteristic of an inertial reference frame. 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 existence), which led to the emergence of such phenomena as the twin paradox. Since the reference systems 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 that who remained on Earth. It is clear that this is physically impossible.
This means that in order to observe relativistic effects, we need some kind of special, dedicated reference system. 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 must (and, without alternative) have the properties of a priority, basic system 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 a failed way to explain the twin paradox
Attempts to explain the priority of the “earthly” 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 reference system. In this case, the reference system associated with the observer on Earth is considered inertial, despite the fact that in physical science it is officially recognized as non-inertial (Dettlaff, Yavorsky, physics course, 2000). This is the first one. 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 an 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 frame of reference, or the observed effects have a different (non-relativistic) explanation. Perhaps the processes are associated with the peculiarities of setting up or interpreting experiments, or with other physical mechanisms of the observed phenomena.
Conclusion
Thus, non-inertial frames of reference lead to the emergence of forces that did not find their place in Newton’s laws of mechanics. When making calculations for non-inertial systems, taking these forces into account is mandatory, including when developing technical products.
One may be afraid that most readers will already be bored with theoretical reasoning and will demand to cite specific example inertial system in nature. We will try to fulfill their wishes as far as possible. Let's consider a specific example: is the Earth an inertial system? Every schoolchild will say to this: “All the examples that the physics teacher gives in class, explaining Newton’s laws, relate to the movement of bodies on Earth. I understand this to mean that the movements of all bodies on Earth occur according to Newton's laws. Therefore, the Earth is an inertial system.”
Yet this conclusion is not accurate. To see this, let us mentally transport ourselves to the Parisian Pantheon, where in 1851 a member of the French Academy of Sciences, Leon Foucault, demonstrated his famous experiment.
A 67-meter cable is suspended from the dome of the Pantheon, to which is attached a copper weight weighing 28 kg. This giant pendulum is set in motion. After just a few oscillations, an amazing phenomenon is discovered: the plane in which the pendulum swings begins to slowly rotate. Why? Foucault explained the result of the experiment by the rotation of the Earth around its axis. The earth rotates, but the plane of the pendulum's swing does not change - this leads to rotation of the plane of the pendulum's oscillations relative to the earth's surface. We completely agree with this explanation, we will just express it a little differently: the Earth is not an inertial system. The plane of oscillation of the pendulum rotates relative to the Earth, but it is impossible to detect any body that would be the source of the force causing this rotation. In this case, acceleration (rotation refers to accelerated movements) occurs without the influence of real force. In inertial systems, where Newton's laws are valid, such phenomena are impossible.
The Earth can be considered an inertial system only approximately; in other words, we can consider the Earth an inertial system only to describe processes on which its rotation has practically no noticeable effect. The overwhelming majority of the phenomena around us are precisely of this nature. Therefore, in practical life we can safely apply Newton’s laws to movements on Earth.
The fact that the Earth is not an inertial system is confirmed by other phenomena. In 1802, an experiment was carried out in Hamburg in which, from a height of 76 m a heavy body fell to the ground. It turned out that the body did not fall exactly in the direction of the gravity acting on it, but deviated almost 1 cm to the east. This can only be explained by the fact that the Earth is a non-inertial system.
In 1857, the Russian academician Karl Baer established the well-known law of erosion of the river bank: for rivers that flow along the meridian in the northern hemisphere, the right bank is high and the left bank is low, in the southern hemisphere, on the contrary, the left bank is high and the right bank is low. This pattern is especially pronounced in big rivers. The Nile, Ob, Irtysh, Lena, Volga, Danube, Dnieper, Don, etc. have a high right bank. The left bank is higher than the right bank of such rivers of the southern hemisphere as the Parana and Paraguay. This can only be explained by the fact that the waters of rivers flowing along the meridians in the northern hemisphere shift to the right (in the southern hemisphere, respectively, to the left), washing away the right bank, and the left bank, formed from washed-up sand, becomes sloping.
Why should rivers flowing along the meridian deviate to the side? For the same reason that the plane of the pendulum rotates and a freely falling body deviates. The geographer will answer that all these phenomena are caused by the rotation of the Earth around its axis. The physicist will explain that this expresses the non-inertiality of the Earth as a body of reference. The Earth rotates relative to inertial systems.
Finding an inertial frame is not difficult in principle: you just need to find a reference frame in which Newton’s laws are satisfied exactly. In practice, it is not at all so simple. An inertial system can only be a system associated with a free body. In nature, as already noted, there are no free bodies; all bodies interact with other bodies, although this interaction can be arbitrarily small. Therefore, it is impossible to indicate a specific inertial system in nature, but it is always possible to find a system that, when studying a given problem, can be considered inertial with sufficient accuracy for practice. The required system should always be chosen so that the phenomena caused by its non-inertiality are less than the error of the used measuring instruments. As we have already noted, when describing most of the earth’s movements, our planet can be considered an inertial system. In Foucault's experiment, as well as in the study of the Earth's motion, the inertial system should be associated with the Sun. The movement of the Sun can be described in an inertial system associated with the surrounding stars (the stars are considered practically motionless), and when studying the rotation of the Galaxy, it is necessary to connect the inertial system with the center of mass of the Galaxy.
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 applies to the simplest case of motion - the movement 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 carry out a single experiment that would pure form showed 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 less and less, and observe what this leads to. You can, for example, observe the movement of a smooth stone on a horizontal surface after it has been given a certain speed. (The attraction of a stone to the ground is balanced by the action of the surface on which it rests, and the speed of its movement is affected only by friction.) It is easy to find that the smoother the surface, the more slowly the speed of the stone will decrease. On smooth ice The stone slides for a very long time without noticeably changing its 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: if the surface were perfectly smooth, then in the absence of air resistance (in a vacuum), the stone would not change its speed at all. It was this conclusion that Galileo first came to.
On the other hand, it is easy to notice that when the speed of a body changes, the influence of other bodies on it is always detected. From this we can come to the conclusion that a body that is sufficiently distant from other bodies and for this reason does not interact with them moves at a constant speed.
Movement is relative, so it makes sense to talk only about the movement of a body in relation to a frame of reference associated with another body. The question immediately arises: will a free body move at a constant speed relative to any other body? The answer, of course, is negative. So, if in relation to the Earth a free body moves rectilinearly 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 with constant speed, at least in relation 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.
That's why Newton's first law can be formulated like this:
There are such reference systems relative to which a body (material point), in the absence of external influences on it (or with their mutual compensation), maintains a state of rest or uniform rectilinear motion.
Inertial reference frame
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 reference systems in a special, privileged position.
Reference systems, 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 very high degree accuracy can be considered an inertial reference frame heliocentric system, in which the origin of coordinates is connected to the Sun, and the axes are directed to certain “fixed” stars. Reference systems rigidly connected to the surface of the Earth, 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, the reference systems associated with the Earth can be considered inertial with sufficient accuracy.
Inertial reference systems are those that move uniformly and rectilinearly relative to some inertial reference frame..
Galileo found 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 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 does not hold are called non-inertial And.
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 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).
Rice. 2
- Literature
- Open Physics 2.5 (http://college.ru/physics/) Physics: Mechanics. 10th grade: Textbook. For in-depth study
physicists / M.M. Balashov, A.I. Gomonova, A.B. Dolitsky and others; Ed. G.Ya. Myakisheva. – M.: Bustard, 2002. – 496 p.
A reference system moving (relative to the stars) uniformly and rectilinearly (i.e., by inertia) is called inertial. It is obvious that there are an innumerable number of such reference systems, since any system moving uniformly and rectilinearly relative to some inertial reference system is also inertial. Reference systems moving (relative to an inertial frame) with acceleration are called non-inertial.
Experience shows that
in all inertial reference systems, all mechanical processes proceed in exactly the same way (under the same conditions). This position, called mechanical principle relativity (or Galileo's principle of relativity), was formulated in 1636 by Galileo. Galileo explained it using the example of mechanical processes taking place in the cabin of a ship floating evenly and rectilinearly along. For an observer in the cabin, the oscillation of the pendulum, the fall of bodies and other mechanical processes proceed in exactly the same way as on a stationary ship. Therefore, by observing these processes, it is impossible to establish either the magnitude of the speed or even the very fact of the ship’s movement. In order to judge the movement of the ship relative to any reference system (for example, the surface of the water), it is necessary to observe this system (see how objects lying on the water move away, etc.).
By the beginning of the 20th century. It turned out that not only mechanical, but also thermal, electrical, optical and all other processes and natural phenomena occur in exactly the same way in all inertial reference systems. On this basis, Einstein formulated the generalized principle of relativity in 1905, later called Einstein’s principle of relativity:
in all inertial reference systems, all physical processes proceed in exactly the same way (under the same conditions).
This principle, along with the principle that the speed of propagation of light in a vacuum is independent of the movement of the light source (see § 20), formed the basis of the special theory of relativity developed by Einstein.
Newton's laws and other laws of dynamics that we have considered are fulfilled only in inertial frames of reference. In non-inertial frames of reference, these laws, generally speaking, are no longer valid. Let's look at a simple example to illustrate the last statement.
A ball of mass lies on a completely smooth platform, moving uniformly and in a straight line, and an observer is located on the same platform. Another observer is standing on Earth near the place where the platform will soon pass. It is obvious that both observers are associated with inertial frames of reference.
Let now, at the moment of passing by the observer associated with the Earth, the platform begin to move with acceleration a, i.e., become a non-inertial frame of reference. In this case, the ball, which was previously at rest relative to the platform, will begin to move (relative to it) with acceleration a, opposite in direction and equal in magnitude to the acceleration acquired by the platform. Let us find out what the behavior of the ball looks like from the points of view of each of the observers.
For an observer associated with the inertial reference frame - the Earth, the ball continues to move uniformly and rectilinearly in full accordance with the law of inertia (since no forces act on it except the force of gravity, balanced by the reaction of the support).
An observer associated with a non-inertial reference system - a platform - sees a different picture: the ball begins to move and acquires acceleration - but without the influence of force (since the observer does not detect the influence of any other bodies on the ball that impart acceleration to the ball). This clearly contradicts the law of inertia. Newton's second law is also not satisfied: having applied it, the observer would have received that (force) and this is impossible, since neither nor a are equal to zero.
It is possible, however, to make the laws of dynamics applicable to describe movements in non-inertial frames of reference if we introduce into consideration forces of a special kind - inertial forces. Then, in our example, the observer associated with the platform can believe that the ball began to move under the influence of inertial force
The introduction of the inertial force allows us to write Newton's second law (and its consequences) in the usual form (see § 7); only by the acting force we must now understand the resultant of “ordinary” forces and forces of inertia
where is the mass of the body, and is its acceleration.
We called inertial forces forces of a “special kind”, firstly, because they act only in non-inertial frames of reference, and, secondly, because for them, unlike “ordinary” forces, it is impossible to indicate the action of which other ones bodies (on the body in question) they are conditioned. Obviously, for this reason, it is impossible to apply Newton’s third law (and its consequences) to inertial forces; this is the third feature of inertial forces.
The inability to indicate individual bodies whose action (on the body in question) causes inertial forces does not mean, of course, that the occurrence of these forces is not at all associated with the action of any material bodies. There are serious reasons to assume that inertial forces are caused by the action of the entire set of bodies in the Universe (the mass of the Universe as a whole).
The fact is that there is a great similarity between the forces of inertia and the forces of gravity: both are proportional to the mass of the body on which they act, and therefore the acceleration imparted to the body by each of these forces does not depend on the mass of the body. Under certain conditions, these forces cannot be distinguished at all. Suppose, for example, that somewhere in outer space a spaceship is moving with acceleration (due to the operation of the engines). The astronaut in it will experience a force pressing him to the “floor” (the rear wall in relation to the direction of movement) of the ship. This force will create exactly the same effect and cause the astronaut the same sensations that would be caused by the corresponding gravitational force.
If an astronaut believes that his ship is moving with acceleration a relative to the Universe, then he will call the force acting on him the force of inertia. If the astronaut considers his ship stationary, and the Universe as rushing past the ship with the same acceleration a, then he will call this force the gravitational force. And both points of view will be completely equal. No experiment carried out inside a ship can prove the correctness of one point of view and the fallacy of the other.
From the considered and other similar examples it follows that the accelerated motion of the reference system is equivalent (in its effect on bodies) to the emergence of the corresponding gravitational forces. This position is called the principle of equivalence of the forces of gravity and inertia (Einstein's principle of equivalence); this principle is the basis general theory relativity.
Inertial forces arise not only in rectilinearly moving, but also in rotating non-inertial reference systems. Let, for example, on a horizontal platform that can rotate around vertical axis, lies a body of mass associated with the center of rotation O rubber cord(Fig. 18). If the platform starts to rotate angular velocity co (and, therefore, will turn into a non-inertial system), then due to friction the body will also be involved in rotation. At the same time, it will move in the radial direction from the center of the platform until the increasing elastic force of the stretching cord stops this movement. Then the body will begin to rotate at a distance from the center O.
From the point of view of an observer associated with the platform, the movement of the ball relative to it is due to some force. This is the force of inertia, since it is not caused by the action of other specific bodies on the ball; it is called the centrifugal force of inertia. It is obvious that the centrifugal force of inertia is equal in magnitude and opposite in direction to the elastic force of the stretched cord, which plays the role of a centripetal force that acts on a body rotating relative to the inertial system (see § 13) Therefore
therefore, the centrifugal force of inertia is proportional to the distance of the body from the axis of rotation.
We emphasize that the centrifugal force of inertia should not be confused with the “ordinary” centrifugal force mentioned at the end of § 13. These are forces of different natures applied to different objects: the centrifugal force of inertia is applied to the body, and the centrifugal force is applied to the connection.
In conclusion, we note that from the position of the principle of equivalence of the forces of gravity and inertia, a simple explanation is given to the action of all centrifugal mechanisms: pumps, separators, etc. (see § 13).
Any centrifugal mechanism can be considered as a rotating non-inertial system, causing the appearance of a gravitational field of a radial configuration, which in a limited area significantly exceeds the terrestrial gravitational field. In this field, denser particles of the rotating medium or particles weakly associated with it move to its periphery (as if they go “to the bottom”).