A frame of reference moving (relative to the stars) uniformly and rectilinearly (i.e., by inertia) is called inertial. Obviously, there are an innumerable number of such reference frames, since any frame moving uniformly and rectilinearly relative to some inertial reference frame is also inertial. Reference frames moving (with respect to the inertial frame) with acceleration are called non-inertial.
Experience shows that
in all inertial frames of reference, all mechanical processes proceed in exactly the same way (under the same conditions).
This position, called the mechanical principle of relativity (or Galileo's principle of relativity), was formulated in 1636 by Galileo. Galileo explained it by the example of mechanical processes taking place in the cabin of a ship sailing evenly and rectilinearly on a calm sea. 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, observing these processes, it is impossible to establish either the magnitude of the speed, or even the very fact of the movement of the ship. In order to judge the movement of the ship with respect to any reference system (for example, the surface of the ocean), it is necessary to observe this system as well (to see how objects lying on the water move away, etc.).
By the beginning of the XX century. it turned out that not only mechanical, but also thermal, electrical, optical and all other processes and phenomena of nature proceed in exactly the same way in all inertial frames of reference. On this basis, Einstein in 1905 formulated the generalized principle of relativity, later called Einstein's principle of relativity:
in all inertial frames of reference, all physical processes proceed in exactly the same way (under the same conditions).
This principle, along with the proposition that the speed of propagation of light in a vacuum is independent of the motion 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 considered by us are fulfilled only in inertial frames of reference. In non-inertial frames of reference, these laws, generally speaking, are no longer valid. Consider a simple example to clarify the last statement.
On a perfectly smooth platform, moving uniformly and rectilinearly, lies a ball of mass on the same platform is an observer. Another observer is standing on Earth not far from where the platform is about to pass. It is obvious that both observers are connected with inertial frames of reference.
Let now, at the moment of passing by an observer connected with the Earth, the platform begin to move with an acceleration a, i.e., it becomes a non-inertial frame of reference. In this case, the ball, which was previously at rest relative to the platform, will begin (relative to it) in motion with an acceleration a, opposite in direction and equal in magnitude to the acceleration acquired by the platform. Let's find out what the behavior of the ball looks like from the point of view of each of the observers.
For an observer associated with an inertial reference system - 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 for gravity, balanced by the reaction of the support).
An observer associated with a non-inertial reference system - a platform, has a different picture: the ball starts moving and acquires acceleration - but without the influence of a force (since the observer does not detect the impact on the ball of any other bodies that impart acceleration to the ball). This clearly contradicts the law of inertia. Newton's second law is also not satisfied: by applying it, the observer would obtain that (force) a this is impossible, since neither nor a are equal to zero.
It is possible, however, to make the laws of dynamics applicable to the description of motions in non-inertial frames of reference, if we introduce into consideration forces of a special kind - the forces of inertia. Then, in our example, the observer connected to the platform can assume that the ball is in motion under the action of the inertia force
The introduction of the force of inertia makes it possible to write down Newton's second law (and its consequences) in the usual form (see § 7); only under the acting force it is now necessary to understand the resultant of the "ordinary" forces and the forces of inertia
where is the mass of the body and is its acceleration.
We called the forces of inertia 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 which other 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 the forces of inertia; this is the third feature of inertial forces.
The impossibility of specifying individual bodies, the action of which (on the body under consideration) is due to the forces of inertia, does not mean, of course, that the emergence of these forces is not at all connected with the action of any material bodies. There are serious reasons to assume that the forces of inertia are due to the action of the entire set of bodies of 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. Let, for example, a spaceship move with acceleration (due to the operation of engines) somewhere in outer space. The cosmonaut in it will experience a force that presses him to the "floor" (the back wall in relation to the direction of movement) of the spacecraft. This force will create exactly the same effect and will cause the same sensations in the astronaut as the corresponding force of gravity would cause.
If an astronaut believes that his ship is moving with an acceleration a relative to the universe, then he will call the force acting on it the force of inertia. If, however, the cosmonaut considers his ship to be motionless, and the Universe to be 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 absolutely equal. No experiment carried out inside the ship can prove the correctness of one and the fallacy of the other point of view.
It follows from the considered and other similar examples that the accelerated motion of the frame of reference is equivalent (by 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 of the general theory of relativity.
Forces of inertia arise not only in rectilinearly moving, but also in rotating non-inertial frames of reference. Let, for example, on a horizontal platform that can rotate around a vertical axis, there is a body of mass connected with the center of rotation O by a rubber cord (Fig. 18). If the platform begins to rotate with an angular velocity ω (and, consequently, turns into a non-inertial system), then due to friction, the body will also be involved in rotation. However, it will move in a 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 connected 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 certain bodies on the ball; it is called the centrifugal force of inertia. Obviously, the centrifugal force of inertia is equal in magnitude and opposite in direction to the elastic force of a stretched cord, which plays the role of a centripetal force that acts on a body rotating with respect to the inertial frame (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 a different nature 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 standpoint of the principle of equivalence of the forces of gravity and inertia, a simple explanation is given to the operation 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 a rotating medium or particles that are weakly bound to it move towards its periphery (as if they go "to the bottom").
inertial frame of reference
Inertial frame of reference(ISO) - a reference frame in which Newton's first law (the law of inertia) is valid: all free bodies (that is, those that are not affected by external forces or the action of these forces is compensated) move rectilinearly and uniformly or rest. Equivalent is the following formulation, convenient for use in theoretical mechanics:
Properties of inertial frames of reference
Any frame of reference moving uniformly and rectilinearly relative to the IFR is also an IFR. According to the principle of relativity, all IFRs are equal, and all laws of physics are invariant with respect to the transition from one IFR 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 set of such systems moving relative to each other with all possible constant velocities. If IFRs 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 conservation of angular momentum, and the homogeneity of time will conserve the energy of a moving body.
If the velocities of the relative motion of IFRs realized by real bodies can take on any values, the connection between the coordinates and times of any "event" in different IFRs is carried out by Galilean transformations.
Connection with real reference systems
Absolutely inertial systems are a mathematical abstraction, which 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 relative exceed 1.5 10 −10 m/s² (at the 1σ level). The accuracy of experiments on the analysis of the arrival time of pulses from pulsars, and soon astrometric measurements, is such that in the near future the acceleration of the solar system should be measured as it moves in the gravitational field of the Galaxy, which is estimated in m/s².
With varying degrees of accuracy and depending on the area of \u200b\u200buse, inertial systems can be considered reference systems associated with: the Earth, the Sun, fixed 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 built according to the following algorithm. The center of the earth is chosen as the point O - the origin of coordinates in accordance with its accepted model. Axis z - 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
see also
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See what the "Inertial Reference System" is in other dictionaries:
Reference system, in which the law of inertia is valid: mater. a point when no forces act on it (or mutually balanced forces act on it), is at rest or uniform rectilinear motion. Any reference system, ... ... Physical Encyclopedia
INERTIAL REFERENCE, see Frame of reference... Modern Encyclopedia
inertial frame of reference- INERTIAL FEEDBACK, see Frame of reference. … Illustrated Encyclopedic Dictionary
inertial frame of reference- inercinė atskaitos sistema statusas T sritis fizika atitikmenys: engl. Galilean frame of reference; inertial reference system vok. inertiales Bezugssystem, n; Inertialsystem, n; Tragheitssystem, n rus. inertial frame of reference, f pranc.… … Fizikos terminų žodynas
A reference system in which the law of inertia is valid: a material point, when no forces act on it (or mutually balanced forces act), is at rest or uniform rectilinear motion. Every… … Great Soviet Encyclopedia
A reference system in which the law of inertia is valid, i.e., a body free from influences from other bodies, retains its speed unchanged (in absolute value and in direction). I. s. about. is such (and only such) reference system, to paradise ... ... Big encyclopedic polytechnic dictionary
A frame of reference in which the law of inertia is valid: a material point, on which no forces act, is at rest or in uniform rectilinear motion. Any frame of reference moving relative to an IS. about. progressively... Natural science. encyclopedic Dictionary
inertial frame of reference- Reference system, in relation to which an isolated material point is at rest or moves in a straight line and uniformly ... Polytechnic terminological explanatory dictionary
A reference system in which the law of inertia is valid: a material point, on which no forces act, is at rest or uniform rectilinear motion. Any frame of reference moving relative to an inertial ... ... encyclopedic Dictionary
Reference system inertial- a frame of reference in which the law of inertia is valid: a material point, when no forces act on it (or mutually balanced forces act), is at rest or uniform rectilinear motion. Every system... Concepts of modern natural science. Glossary of basic terms
Any body can be influenced by other bodies surrounding it, as a result of which the state of motion (rest) of the observed body can change. At the same time, such impacts can be compensated (balanced) and not cause such changes. When it is said that the actions of two or more bodies compensate each other, this means that the result of their joint action is the same as if these bodies did not exist at all. If the influence of other bodies on the body is compensated, then relative to the Earth the body is either at rest or moves in a straight line and uniformly.
Thus, we come to one of the fundamental laws of mechanics, which is called Newton's first law.
Newton's 1st law (law of inertia)
There are such reference systems in which a translationally moving body is at rest or uniform rectilinear motion (motion by inertia) until the influences from other bodies take it out of this state.
In relation to what has been said, a change in the speed of a body (ie, acceleration) is always caused by the impact of some other bodies on this body.
Newton's 1st law is valid only in inertial frames of reference.
Definition
Frames of reference, relative to which a body that is not affected by other bodies, is at rest or moves uniformly and rectilinearly, are called inertial.
It is possible to determine whether a given frame of reference is inertial only empirically. In most cases, one can consider inertial frames of reference associated with the Earth or with reference bodies that move uniformly and rectilinearly with respect to the earth's surface.
Figure 1. Inertial frames of reference
At present, it has been experimentally confirmed that the heliocentric frame of reference associated with the center of the Sun and three "fixed" stars is practically inertial.
Any other frame of reference moving uniformly and rectilinearly relative to the inertial one is itself inertial.
Galileo established that it is impossible to determine whether this system is at rest or moving uniformly and rectilinearly by any mechanical experiments set up inside an inertial frame of reference. This statement is called Galileo's principle of relativity, or the mechanical principle of relativity.
This principle was subsequently developed by A. Einstein and is one of the postulates of the special theory of relativity. ISOs 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 ISO.
If the reference body moves with acceleration, then the reference frame associated with it is non-inertial, and Newton's 1st law is not valid in it.
The property of bodies to maintain their state in time (speed of movement, direction of movement, state of rest, etc.) is called inertia. The very phenomenon of conservation of speed by a moving body in the absence of external influences is called inertia.
Figure 2. Manifestations of inertia in the bus at the start of movement and braking
With the manifestation of the inertia of bodies, we often meet in everyday life. With a sharp acceleration of the bus, the passengers in it lean back (Fig. 2, a), and with a sharp braking of the bus, they lean forward (Fig. 2, b), and when the bus turns to the right - to its left wall. With a large acceleration of a take-off aircraft, the pilot's body, trying to maintain its original state of rest, is pressed against the seat.
The inertia of the bodies is clearly manifested in a sharp change in the acceleration of the bodies of the system, when the inertial frame of reference is replaced by a non-inertial one, and vice versa.
The inertia of a body is usually characterized by its mass (inertial mass).
The force acting on the body from a non-inertial frame of reference is called the force of inertia
If several forces simultaneously act on a body in a non-inertial reference frame, some of which are "ordinary" forces, and others are inertial, then the body will experience one resultant force, which is the vector sum of all forces acting on it. This resultant force is not a force of inertia. The force of inertia is only a component of the resulting force.
If a stick, suspended on two thin threads, is slowly pulled by a cord attached to its center, then:
- the wand will break;
- the cord breaks;
- one of the threads will break;
- any option is possible, depending on the applied force
Figure 4
The force is applied to the middle of the stick, at the place where the cord hangs. Since, according to Newton's 1st law, any body has inertia, a part of the stick at the point of suspension of the cord will move under the action of the applied force, and other parts of the stick, on which the force does not act, will remain at rest. Therefore, the stick will break at the point of suspension.
Answer. Correct answer 1.
A man pulls two tied sledges, applying force at an angle of 300 to the horizon. Find this force if it is known that the sleigh moves uniformly. The weight of the sleigh is 40 kg. Friction coefficient 0.3.
$t_1$ = $t_2$ = $m$ = 40 kg
$(\mathbf \mu )$ = 0.3
$(\mathbf \alpha )$=$30^(\circ)$
$g$ = 9.8 m/s2
Figure 5
Since the sleigh is moving at a constant speed, according to Newton's first law, the sum of the forces acting on the sleigh is zero. Let's write Newton's first law for each body immediately in projection on the axis, and add Coulomb's law of dry friction for the sleigh:
OX axis OY axis
\[\left\( \begin(array)(c) T-F_(tr1)=0 \\ F_(tr1)=\mu N_1 \\ F_(tr2)=\mu N_2 \\ F(cos \alpha - \ )F_(tr2)-T=0 \end(array) \right.\left\( \begin(array)(c) N_1-mg=0 \\ N_2+F(sin \alpha \ )-mg=0 \end(array) \right.\]
$F=\frac(2\mu mg)((cos \alpha \ )+\mu (sin \alpha \ ))=\ \frac(2\cdot 0.3\cdot 40\cdot 9.8)((cos 30() ^\circ \ )+0.3\cdot (sin 30()^\circ \ ))=231.5\ H$
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, amendments are added to the classical laws of mechanics. 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 to be 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 a simple example of a non-inertial frame of reference as 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 force of 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 a real acting 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 in various 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 of the action of centrifugal forces is the rotation on a 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 has a great 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 of the special theory of 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 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 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. At the same time, 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 the spacecraft 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.
Questions.
1. How does a body move if no other bodies act on it?
The body moves uniformly and rectilinearly, or is at rest.
2. The body moves in a straight line uniformly. Does it change its speed?
If a body moves uniformly and in a straight line, then its speed does not change.
3. What views regarding the state of rest and movement of bodies existed before the beginning of the 17th century?
Until the beginning of the 17th century, Aristotle's theory dominated, according to which, if there is no external influence on it, then it can rest, and in order for it to move at a constant speed, another body must continuously act on it.
4. How does Galileo's point of view regarding the motion of bodies differ from Aristotle's point of view?
Galileo's point of view on the motion of bodies differs from Aristotle's point of view in that bodies can move in the absence of external forces.
5. How was the experiment shown in Figure 19 carried out, and what conclusions follow from it?
The course of experience. There are two balls on a trolley moving uniformly and rectilinearly relative to the ground. One ball rests on the bottom of the cart, and the second is suspended from a thread. The balls are at rest relative to the cart, since the forces acting on them are balanced. When braking, both balls come into motion. They change their speed relative to the cart, although no forces act on them. Conclusion: Consequently, in the frame of reference associated with the braking cart, the law of inertia is not fulfilled.
6. How is Newton's first law read? (in modern terms)?
Newton's first law in the modern formulation: there are reference systems with respect to which bodies keep their speed unchanged if they are not affected by other bodies (forces) or the action of these bodies (forces) is compensated (equal to zero).
7. What reference systems are called inertial, and which are non-inertial?
Frames of reference in which the law of inertia is fulfilled are called inertial, and in which it is not fulfilled - non-inertial.
Yes, you can. This follows from the definition of inertial frames of reference.
9. Is the frame of reference moving with acceleration relative to any inertial frame?
No, not inertial.
Exercises.
1. On the table, in a uniformly and rectilinearly moving train, there is an easily movable toy car. When the train braked, the car rolled forward without any external influence, maintaining its speed relative to the ground.
Is the law of inertia fulfilled: a) in the reference frame connected with the earth; b) in the frame of reference associated with the train, during its rectilinear and uniform motion? During braking?
Is it possible in the described case to consider the frame of reference connected with the earth to be inertial? with a train?
a) Yes, the law of inertia is satisfied in all cases, because the machine continued to move relative to the Earth; b) In the case of uniform and rectilinear motion of the train, the law of inertia is satisfied (the machine is stationary), but not when braking. The earth in all cases is an inertial frame of reference, and the train is only in uniform and rectilinear motion.
