Mathematically, the movement of a body (or material point) in relation to the selected frame of reference is described by equations that establish how they change over time t coordinates defining the position of the body (point) in this frame of reference. These equations are called equations of motion. For example, in Cartesian coordinates x, y, z, the motion of a point is determined by the equations x \u003d f 1 (t) (\\ displaystyle x \u003d f_ (1) (t)), y \u003d f 2 (t) (\\ displaystyle y \u003d f_ (2) (t)), z \u003d f 3 (t) (\\ displaystyle z \u003d f_ (3) (t)).

In modern physics, any movement is considered relative, and the movement of a body should be considered only in relation to some other body (reference body) or a system of bodies. It is impossible to indicate, for example, how the Moon moves in general, you can only determine its movement, for example, in relation to the Earth, the Sun, the stars, etc.

Other definitions

On the other hand, it was previously believed that there is a certain "fundamental" frame of reference, the simplicity of writing in which the laws of nature distinguish it from all other systems. So, Newton considered absolute space to be the selected frame of reference, and physicists of the 19th century believed that the system with respect to which the ether of Maxwell's electrodynamics rests is privileged, and therefore it was called the absolute frame of reference (ARF). Finally, the assumptions about the existence of a privileged frame of reference were rejected by the theory of relativity. In modern concepts, no absolute frame of reference exists, since the laws of nature, expressed in tensor form, have the same form in all frames of reference - that is, at all points in space and at all times. This condition - local space-time invariance - is one of the testable foundations of physics.

Sometimes an absolute reference frame is called a system associated with relic radiation, that is, an inertial reference frame in which relict radiation has no dipole anisotropy.

Reference body

In physics, a reference body is a set of bodies motionless relative to each other, in relation to which the motion is considered (in the related

The relativity of motion lies in the fact that when studying motion in frames of reference moving uniformly and rectilinearly relative to the adopted stationary frame of reference, all calculations can be carried out using the same formulas and equations, as if there were no motion of the moving frame of reference relative to the stationary one.

Motion Relativity: Basics

Frame of reference is a set of a reference body, coordinate system and time associated with the body, in relation to which the movement (or balance) of some other material points or bodies is studied. Any movement is relative, and the movement of a body should be considered only in relation to some other body (reference body) or a system of bodies. It is impossible to indicate, for example, how the moon moves in general, one can only determine its movement in relation to the Earth or the Sun and the stars, etc.

Mathematically, the movement of a body (or material point) in relation to the selected frame of reference is described by equations that establish how the coordinates change over time t, which determine the position of the body (point) in this frame of reference. For example, in Cartesian coordinates x, y, z, the motion of a point is determined by the equations X \u003d f1 (t), y \u003d f2 (t), Z \u003d f3 (t), are called equations of motion.

Reference body - the body with respect to which the frame of reference is set.

Frame of reference - compared with the continuum stretched over real or imaginary basic reference bodies. It is natural to present the following two requirements to the basic (generating) bodies of the reference frame:

1. Basic bodies must be motionless relative to each other. This is checked, for example, by the absence of the Doppler effect when exchanging radio signals between them.

2. Basic bodies must move with the same acceleration, that is, have the same indicators of accelerometers installed on them.

Moving bodies change their position relative to other bodies. The position of a car rushing along the highway changes relative to the signs on the kilometer posts, the position of a ship sailing in the sea near the coast changes relative to the stars and the coastline, and the movement of an aircraft flying over the ground can be judged by its change in position relative to the Earth's surface. Mechanical movement is the process of changing the position of bodies in space over time. It can be shown that the same body can move in different ways relative to other bodies.

Thus, it is possible to say that some body is moving only when it is clear with respect to which other body - the reference body its position has changed.

Relativity of movement: an example from life

Imagine a train. She rides quietly on the rails, carrying passengers to their dachas. And suddenly, sitting in the last carriage, a hooligan and parasite Sidorov notices that controllers are entering the car at the Sady station. Naturally, Sidorov did not buy a ticket, and he wants to pay the fine even less.

And so, so that he would not be caught, he quickly makes a movement in a straight-line uniform movement to another car. The controllers, having checked the tickets of all passengers, move in the same direction. Sidorov goes to the next car again and so on. And so, when he reaches the first carriage and there is nowhere to go further, it turns out that the train has just reached the Ogorody station, which he needs, and a happy Sidorov gets out, rejoicing that he passed by a hare and did not get caught.

What can we learn from this action-packed story? We can, without a doubt, be happy for Sidorov, or we can, moreover, discover another interesting fact.

While the train traveled five kilometers from the Sady station to the Ogorody station in five minutes, the hare Sidorov covered the same distance plus the distance in the same time, equal to length the train in which he was traveling, that is, about five thousand two hundred meters in the same five minutes. It turns out that Sidorov was moving faster than the electric train. However, the controllers following on his heels developed the same speed. Considering that the speed of the train was about 60 km / h, it was just right to give them all several Olympic medals.

However, of course, no one will engage in such stupidity, because everyone understands that Sidorov's incredible speed was developed by him only relative to stationary stations, rails and vegetable gardens, and this speed was due to the movement of the train, and not at all the incredible abilities of Sidorov. Regarding the train, Sidorov did not move at all fast and did not reach not only the Olympic medal, but even the ribbon from it. This is where we come across such a concept as the relativity of motion.

Can you be stationary and still move faster than a Formula 1 car? It turns out you can. Any movement depends on the choice of a frame of reference, that is, any movement is relative. The topic of today's lesson is “Relativity of motion. The law of addition of displacements and speeds. " We will learn how to choose a frame of reference in a particular case, how to find the movement and speed of a body.

Mechanical movement is the change in the position of a body in space relative to other bodies over time. In this definition, the key phrase is "relative to other bodies." Each of us is motionless relative to some surface, but relative to the Sun, we make orbital motion together with the entire Earth at a speed of 30 km / s, that is, the motion depends on the frame of reference.

Reference system - a set of coordinates and clocks associated with the body, relative to which the movement is studied. For example, when describing the movement of passengers in the passenger compartment of a car, the reference system can be associated with a roadside cafe, or it can be associated with the interior of a car or with a moving oncoming car, if we estimate the overtaking time (Fig. 1).

Figure: 1. Choice of frame of reference

What are physical quantities and the concepts depend on the choice of the frame of reference?

1. Position or coordinates of the body

Consider an arbitrary point. In different systems, it has different coordinates (Fig. 2).

Figure: 2. The coordinates of the point in different systems coordinates

2. Trajectory

Consider the trajectory of a point located on the propeller of an aircraft in two reference systems: the reference frame associated with the pilot and the reference frame associated with the observer on Earth. For the pilot, this point will make a circular rotation (Fig. 3).

Figure: 3. Circular rotation

Whereas for an observer on Earth, the trajectory of this point will be a helix (Fig. 4). Obviously, the trajectory depends on the choice of the frame of reference.

Figure: 4. Helical trajectory

Trajectory relativity. Body motion trajectories in different reference systems

Let us consider how the trajectory of motion changes depending on the choice of the frame of reference using the example of the problem.

A task

What will be the trajectory of the point at the end of the propeller in different COs?

1. In CO associated with the pilot of the aircraft.

2. In CO associated with an observer on Earth.

Decision:

1. Neither the pilot nor the propeller moves relative to the aircraft. For the pilot, the trajectory of the point will appear to be a circle (Fig. 5).

Figure: 5. Trajectory of the point relative to the pilot

2. For an observer on Earth, a point moves in two ways: rotating and moving forward. The trajectory will be helical (Fig. 6).

Figure: 6. Trajectory of a point relative to an observer on Earth

Answer : 1) a circle; 2) helix.

Using this problem as an example, we made sure that the trajectory is a relative concept.

As an independent check, we suggest you solve the following problem:

What will be the trajectory of a point at the end of the wheel relative to the center of the wheel, if this wheel is moving forward, and relative to points on the ground (stationary observer)?

3. Moving and path

Consider a situation when a raft is floating and at some point a swimmer jumps off it and seeks to cross to the opposite bank. The movement of the swimmer relative to the fisherman sitting on the shore and relative to the raft will be different (Fig. 7).

Displacement relative to the earth is called absolute, and relative to a moving body is called relative. The movement of a moving body (raft) relative to a stationary body (fisherman) is called portable.

Figure: 7. Moving the swimmer

From the example it follows that displacement and path are relative values.

4. Speed

Using the previous example, you can easily show that speed is also a relative value. After all, speed is the ratio of movement to time. Our time is the same, but the movement is different. Therefore, the speed will be different.

The dependence of the characteristics of motion on the choice of the frame of reference is called relativity of motion.

In the history of mankind, there have been dramatic cases related precisely to the choice of the frame of reference. The execution of Giordano Bruno, the abdication of Galileo Galilei - all these are the consequences of the struggle between the supporters of the geocentric frame of reference and the heliocentric frame of reference. It was very difficult for mankind to get used to the idea that the Earth is not at all the center of the universe, but a completely ordinary planet. And the movement can be considered not only relative to the Earth, this movement will be absolute and relative to the Sun, stars or any other bodies. Describe movement celestial bodies in the frame of reference associated with the Sun, it is much more convenient and simpler, this was convincingly shown first by Kepler, and then by Newton, who, on the basis of considering the motion of the Moon around the Earth, derived his famous law of universal gravitation.

If we say that the trajectory, path, displacement and speed are relative, that is, they depend on the choice of the frame of reference, then we do not say this about time. In the framework of classical, or Newtonian, mechanics, time is an absolute value, that is, it flows in all reference frames in the same way.

Let's consider how to find displacement and speed in one frame of reference, if they are known to us in another frame.

Consider the previous situation, when a raft is floating and at some point a swimmer jumps off it and seeks to cross to the opposite bank.

How is the movement of the swimmer relative to the stationary CO (connected with the fisherman) connected with the movement of the relatively mobile CO (connected to the raft) (Fig. 8)?

Figure: 8. Illustration for the problem

We called the movement in a fixed frame of reference. From the triangle of vectors it follows that ... Now let's move on to finding the relationship between speeds. Let us recall that in the framework of Newtonian mechanics, time is an absolute value (time flows in all reference frames in the same way). This means that each term from the previous equality can be divided by time. We get:

This is the speed at which a swimmer moves to a fisherman;

This is the swimmer's own speed;

This is the speed of the raft (the speed of the river flow).

The problem for the law of addition of velocities

Let's consider the law of addition of velocities using the example of the problem.

A task

Two cars are moving towards each other: the first car with speed, the second - with speed. How fast are the cars approaching (Fig. 9)?

Figure: 9. Illustration for the problem

Decision

Let's apply the law of addition of velocities. To do this, we will move from the usual CO associated with the Earth to the CO associated with the first car. Thus, the first car becomes stationary, while the second moves towards it at a speed (relative speed). At what speed, if the first car is stationary, revolves around the first car, the Earth? It rotates at the speed and the speed is directed in the direction of the speed of the second car (portable speed). Two vectors that are directed along one straight line are added. ...

Answer: .

The limits of applicability of the law of addition of velocities. The law of addition of velocities in the theory of relativity

For a long time it was believed that the classical law of addition of velocities is always valid and applicable to all reference frames. However, about years ago it turned out that in some situations this law does not work. Let us consider such a case using the example of a problem.

Imagine that you are on a space rocket that is moving at a speed. And the captain of the space rocket turns on the flashlight in the direction of the rocket (Fig. 10). The speed of propagation of light in a vacuum is. What will be the speed of light for a stationary observer on Earth? Will it be equal to the sum of the speeds of light and rocket?

Figure: 10. Illustration for the problem

The fact is that physics is faced with two conflicting concepts here. On the one hand, according to Maxwell's electrodynamics, the maximum speed is the speed of light, and it is equal. On the other hand, according to Newtonian mechanics, time is an absolute value. The problem was solved when Einstein proposed the special theory of relativity, or rather its postulates. He was the first to suggest that time is not absolute. That is, somewhere it flows faster, and somewhere slower. Of course, in our world of low speeds, we do not notice this effect. In order to feel this difference, we need to move at speeds close to the speed of light. Based on Einstein's conclusions, the law of addition of velocities was obtained in the special theory of relativity. It looks like this:

This is the speed of a relatively stationary CO;

This is the speed of a relatively mobile CO;

This is the speed of the moving CO relative to the stationary CO.

If we substitute the values \u200b\u200bfrom our problem, then we get that the speed of light for a stationary observer on Earth will be.

The controversy was resolved. You can also make sure that if the speeds are very small compared to the speed of light, then the formula for the theory of relativity goes over into the classical formula for adding the speeds.

In most cases, we will use the classic law.

Today we have found out that movement depends on the frame of reference, that speed, path, movement and trajectory are relative concepts. And time in the framework of classical mechanics is an absolute concept. We learned to apply the knowledge gained by examining some typical examples.

List of references

1. Tikhomirova S.A., Yavorsky B.M. Physics (basic level) - M .: Mnemosina, 2012.
2. Gendenshtein L.E., Dick Yu.I. Physics grade 10. - M .: Mnemosina, 2014.
3. Kikoin I.K., Kikoin A.K. Physics - 9, Moscow, Education, 1990.

1. Internet portal Class-fizika.narod.ru ().
2. Internet portal Nado5.ru ().
3. Internet portal Fizika.ayp.ru ().

Homework

1. Give a definition of the relativity of motion.
2. What physical quantities depend on the choice of the frame of reference?

Relativity of mechanical movement

Movement in physics is the movement of a body in space, which has its own specific features.

Mechanical movement can be represented as a change in the position of a particular material body in space. All changes should occur relative to each other over time.

Types of mechanical movement

Mechanical movement is of three main types:

• rectilinear movement;
• uniform movement;
• curvilinear movement.

To solve problems in physics, it is customary to use assumptions in the form of representing an object by a material point. This makes sense in cases where the shape, size and body can be ignored in its true parameters and choose the object under study in the form of a certain point.

There are several basic conditions when the method of introducing a material point is used in solving a problem:

• in cases where the dimensions of the body are extremely small in relation to the distance that it travels;
• in cases where the body is moving forward.

The translational motion occurs at the moment when all points of the material body move in the same way. Also, the body will move in a translational manner when a straight line is drawn through two points of this object, and it should move parallel to its original location.

At the beginning of the study of the relativity of mechanical motion, the concept of a frame of reference is introduced. It is formed together with a reference body and a coordinate system, including a clock for counting the time of movement. All elements form a single frame of reference.

Frame of reference

Remark 2

The reference body is such a body, relative to which the position of other bodies in motion is determined.

If you do not set additional data in solving the problem of calculating mechanical motion, then it will not be possible to notice it, since all body movements are calculated relative to the interaction with other physical bodies.

Scientists have introduced additional concepts to understand the phenomenon, including:

• rectilinear uniform movement;
• the speed of movement of the body.

With their help, the researchers tried to figure out how the body moved in space. In particular, it was possible to determine the type of body motion relative to observers who had different speeds. It turned out that the observation result depends on the ratio of the velocities of the body and the observers relative to each other. All calculations used the formulas of classical mechanics.

There are several basic reference systems that are used when solving problems:

• movable;
• motionless;
• inertial.

When considering motion relative to a moving frame of reference, the classical law of addition of velocities is used. The speed of the body relative to the stationary frame of reference will be equal to the vector sum of the speed of the body relative to the moving frame of reference, as well as the speed of the moving frame of reference relative to the stationary one.

$ \\ overline (v) \u003d \\ overline (v_ (0)) + \\ overline (v_ (s)) $, where:

• $ \\ overline (v) $ - speed of the body in a fixed frame of reference,
• $ \\ overline (v_ (0)) $ is the speed of the body in the moving frame of reference,
• $ \\ overline (v_ (s)) $ is the speed of an additional factor that affects the determination of speed.

The relativity of mechanical motion is the relativity of the speeds with which bodies move. The velocities of bodies relative to different reference systems will also differ. For example, the speed of a person in a train or airplane will differ depending on the frame of reference in which these speeds are determined.

The speeds differ in direction and magnitude. Determination of a specific object of research during mechanical movement plays an important role in calculating the parameters of the movement of a material point. Velocities can be determined in a frame of reference that is associated with a moving vehicle, and can be in relative dependence on a stationary Earth or its rotation in orbit in space.

This situation can be modeled on simple example... Moving on railroad the train will perform mechanical movements relative to another train, which moves on parallel tracks or relative to the Earth. The solution to the problem depends directly on the selected frame of reference. Different frames of reference will have different trajectories. In mechanical motion, the trajectory is also relative. The path traveled by the body depends on the selected frame of reference. In mechanical motion, the path is relative.

Development of the relativity of mechanical motion

Also, according to the law of inertia, began to form inertial reference systems.

The process of realizing the relativity of mechanical movement took a considerable historical period of time. If at first the model of the geocentric system of the world (the Earth is the center of the Universe) was considered acceptable for a long time, then the motion of bodies in different frames of reference began to be considered at the time of the famous scientist Nicolaus Copernicus, who formed the heliocentric model of the world. According to her, the planets Solar system rotate around the sun, and also rotate around their own axis.

The structure of the reference system changed, which later led to the construction of a progressive heliocentric system. This model today makes it possible to solve various scientific goals and problems, including in the field of applied astronomy, when the trajectories of motion of stars, planets, galaxies are calculated based on the method of relativity.

At the beginning of the 20th century, the theory of relativity was formulated, which is also based on the fundamental principles of mechanical motion and interaction of bodies.

All formulas that are used to calculate the mechanical movements of bodies and determine their speed make sense at speeds less than the speed of light in a vacuum.

DEFINITION

Motion relativity manifests itself in the fact that the behavior of any moving body can be determined only in relation to some other body, which is called the reference body.

Reference body and coordinate system

The reference body is chosen arbitrarily. It should be noted that the moving body and the reference body are equal. When calculating motion, each of them, if necessary, can be considered either as a reference body or as a moving body. For example, a person stands on Earth and watches a car driving along the road. A person is motionless relative to the Earth and considers the Earth to be the reference body, the plane and the car in this case are moving bodies. However, the passenger of the car who says that the road is running away from under the wheels is also right. He considers the car to be the reference body (it is motionless relative to the car), while the Earth is a moving body.

To fix the change in the position of the body in space, a coordinate system must be associated with the reference body. A coordinate system is a way of specifying the position of an object in space.

When solving physical problems, the most common is the Cartesian rectangular coordinate system with three mutually perpendicular rectilinear axes - the abscissa (), ordinate () and applicate (). The scale unit for measuring length in SI is the meter.

When navigating the terrain, use the polar coordinate system. The map determines the distance to the desired settlement... The direction of movement is determined by the azimuth, i.e. an angle that makes up direction zero with a line connecting the person to the desired point. Thus, in a polar coordinate system, the coordinates are distance and angle.

In geography, astronomy and in calculating the motions of satellites and spaceships the position of all bodies is determined relative to the center of the Earth in a spherical coordinate system. To determine the position of a point in space in a spherical coordinate system, set the distance to the origin and the angles and are the angles that make up the radius vector with the plane of the zero Greenwich meridian (longitude) and the equatorial plane (latitude).

Frame of reference

The coordinate system, the reference body with which it is connected, and the device for measuring time form a reference frame relative to which the body's movement is considered.

When solving any problem of motion, first of all, the frame of reference in which the motion will be considered must be indicated.

When considering motion relative to a moving frame of reference, the classical law of addition of velocities is valid: the speed of a body relative to a stationary frame of reference is equal to the vector sum of the speed of a body relative to a moving frame of reference and the speed of a moving frame of reference relative to a fixed one:

Examples of solving problems on the topic "Relativity of motion"

EXAMPLE