There is mechanical movement. Relativity of mechanical motion

Lecture 2. Relativity of mechanical motion. Reference systems. Characteristics of mechanical movement: movement, speed, acceleration.

Mechanics - the branch of physics that deals with mechanical motion.

Mechanics is divided into kinematics, dynamics and statics.

Kinematics is a branch of mechanics in which the movement of bodies is considered without clarifying the causes of this movement.Kinematics studies ways of describing movement and the relationship between the quantities that characterize these movements.

The task of kinematics: determination of the kinematic characteristics of movement (trajectory of movement, displacement, distance traveled, coordinates, speed and acceleration of the body), as well as obtaining equations for the dependence of these characteristics on time.

mechanical movement of the body called the change in its position in space relative to other bodies over time.

mechanical movement relatively , the expression "the body moves" is meaningless until it is determined in relation to what the movement is considered. The motion of the same body relative to different bodies turns out to be different. To describe the movement of a body, it is necessary to indicate in relation to which body the movement is considered. This body is calledreference body . Rest is also relative (examples: a passenger in a train at rest looks at a train passing by)

The main task of mechanics – be able to calculate the coordinates of body points at any time.

To solve this, you need to have a body from which the coordinates are counted, associate a coordinate system with it and have a device for measuring time intervals.

The coordinate system, the body of reference with which it is associated, and the instrument for measuring time form reference system , relative to which the motion of the body is considered.

Coordinate systems there are:

1. one-dimensional – the position of the body on the straight line is determined by one coordinate x.

2. two-dimensional – the position of a point on the plane is determined by two coordinates x and y.

3. three-dimensional – the position of a point in space is determined by three coordinates x, y and z.

Every body has a certain size. Different parts of the body are in different places in space. However, in many problems of mechanics there is no need to indicate the positions of individual parts of the body. If the dimensions of the body are small compared to the distances to other bodies, then this body can be considered its material point. This can be done, for example, when studying the motion of planets around the Sun.

If all parts of the body move in the same way, then such a movement is called translational.

For example, cabins in the Giant Wheel attraction, a car on a straight section of the track, etc. move forward. When the body moves forward, it can also be considered as a material point.

material pointa body is called, the dimensions of which, under given conditions, can be neglected .

The concept of a material point plays an important role in mechanics. A body can be considered as a material point if its dimensions are small compared to the distance it travels, or compared to the distance from it to other bodies.

Example . The dimensions of an orbital station in orbit near the Earth can be ignored, and when calculating the trajectory of the spacecraft when docking with the station, one cannot do without taking into account its dimensions.

Characteristics of mechanical movement: movement, speed, acceleration.

Mechanical motion is characterized by three physical quantities:displacement, speed and acceleration.

Moving over time from one point to another, the body (material point) describes a certain line, which is called the trajectory of the body.

The line along which the point of the body moves is called trajectory of movement.

The length of the trajectory is called traveled way.

Denotedl, measured inmeters . (trajectory - trace, path - distance)

Distance traveled l is equal to the length of the arc of the trajectory traversed by the body in some time t.Way – scalar .

By moving the body called a directed segment of a straight line connecting the initial position of the body with its subsequent position. Displacement is a vector quantity.

The vector connecting the start and end points of the trajectory is called movement.

DenotedS , measured in meters. (displacement is a vector, displacement modulus is a scalar)

Speed ​​- a vector physical quantity that characterizes the speed of movement of a body, numerically equal to the ratio of movement in a small period of time to the value of this period.

Denoted v

Speed ​​formula:or

Unit of measurement in SI -m/s .

In practice, the speed unit used is km/h (36 km/h = 10 m/s).

Measure the speedspeedometer .

Acceleration - a vector physical quantity characterizing the rate of change of speed, numerically equal to the ratio of the change in speed to the period of time during which this change occurred.

If the speed changes the same throughout the entire time of movement, then the acceleration can be calculated by the formula:

Acceleration is measuredaccelerometer

SI unitm/s 2

Thus, the main physical quantities in the kinematics of a material point are the distance traveledl, displacement, speed and acceleration. Wayl is a scalar quantity. Displacement, speed and acceleration are vector quantities. To specify a vector quantity, you need to specify its modulus and specify the direction. Vector quantities obey certain mathematical rules. Vectors can be projected onto coordinate axes, they can be added, subtracted, etc.

Relativity of mechanical motion.

Mechanical movement is relative. The motion of the same body relative to different bodies turns out to be different.

For example, a car is moving on a road. There are people in the car. People move along with the car on the road. That is, people move in space relative to the road. But relative to the car itself, people do not move. This manifests itself.

To describe the movement of a body, it is necessary to indicate in relation to which body the movement is considered. This body is called the reference body. Peace is also relative. For example, a passenger on a train at rest looks at a passing train and does not realize which train is moving until they look at the sky or the ground.

All bodies in the universe are moving, so there are no bodies that are in absolute rest. For the same reason, it is possible to determine whether a body is moving or not only relative to some other body.

For example, a car is moving on a road. The road is on the planet Earth. The road is motionless. Therefore, it is possible to measure the speed of a vehicle relative to a stationary road. But the road is stationary relative to the Earth. However, the Earth itself revolves around the Sun. Therefore, the road, along with the car, also revolves around the sun. Consequently, the car performs not only translational motion, but also rotational (relative to the Sun). But relative to the Earth, the car makes only translational motion. This manifests itselfrelativity of mechanical motion .

The motion of the same body may look different from the point of view of different observers. The speed, direction of movement and the type of body trajectory will be different for different observers. Without specifying the reference body, talking about motion is meaningless. For example, a seated passenger in a train is at rest relative to the carriage, but moves with the carriage relative to the station platform.

Let us now illustrate for different observers the difference in the form of the trajectory of a moving body. Being on Earth, in the night sky you can easily see bright fast-flying dots - satellites. They move in circular orbits around the Earth, that is, around us. Let's sit down now spaceship flying towards the sun. We will see that now each satellite moves not in a circle around the Earth, but in a spiral around the Sun:

Relativity of mechanical motion – this is the dependence of the trajectory of the body, the distance traveled, displacement and speed on the choice reference systems .

The movement of bodies can be described in various systems ah countdown. From the point of view of kinematics, all frames of reference are equal. However, the kinematic characteristics of motion, such as trajectory, displacement, speed, turn out to be different in different systems. The quantities that depend on the choice of the reference frame in which they are measured are called relative.

Galileo showed that under the conditions of the Earth it is practically validlaw of inertia. According to this law, the action of forces on a body is manifested in changes in speed; to maintain the same movement with a constant magnitude and direction of speed does not require the presence of forces.Frames of reference in which the law of inertia is satisfied, began to be called inertial reference systems (ISO) .

Systems that rotate or accelerate are non-inertial.

The earth cannot be considered completely ISO: it rotates, but for most of our purposesreference systems associated with the Earth, in a fairly good approximation, can be taken as inertial. A reference frame moving uniformly and rectilinearly relative to the IFR is also inertial.

G. Galileo and I. Newton were deeply aware of what we call todaythe principle of relativity , Whereby mechanical laws physicists must be the same in all ISOs under the same initial conditions.

From this it follows: no ISO is no different from another frame of reference. All ISOs are equivalent in terms of mechanical phenomena.

Galileo's principle of relativity comes from some assumptions that are based on our daily experience. In classical mechanicsspace Andtime consideredabsolute . It is assumed that the length of the bodies is the same in any frame of reference and that time flows in the same way in different frames of reference. It is assumed thatweight body and alsoall forces remain unchanged when moving from one ISO to another.

We are convinced of the validity of the principle of relativity by everyday experience, for example, in a uniformly moving train or plane, bodies move in the same way as on Earth.

There is no experiment that can be used to establish which frame of reference is really at rest and which is moving. There are no frames of reference in a state of absolute rest.

If a coin is tossed vertically upwards on a moving cart, then only the coordinate of the OS will change in the frame of reference associated with the cart.

In the reference system associated with the Earth, the coordinates of the OU and OX change.

Consequently, the position of bodies and their velocities in different frames of reference are different.

Consider the motion of the same body with respect to two different frames of reference: stationary and moving.

A boat crosses a river perpendicular to the flow of the river, moving at a certain speed relative to the water. The movement of the boat is monitored by 2 observers: one motionless on the shore, the other on a raft floating downstream. Relative to the water, the raft is motionless, and relative to the shore, it moves at the speed of the current.

Associate a coordinate system with each observer.

X0Y is a fixed coordinate system.

X'0'Y' – moving coordinate system.

S is the displacement of the boat relative to the fixed CO.

S 1 – movement of the boat relative to the mobile CO

S 2 – movement of the moving frame of reference relative to the fixed reference frame.

According to the law of vector addition

We get the speed by dividing S by t:

v is the speed of the body relative to the stationary CO

v 1 - the speed of the body relative to the mobile CO

v 2 is the speed of the moving reference frame relative to the fixed reference frame

This formula expressesclassical law of addition of velocities: the speed of the body relative to the stationary CO is equal to the geometric sum of the speed of the body relative to the mobile CO and the speed of the mobile CO relative to the stationary CO.

In scalar form, the formula will look like:

This formula was first obtained by Galileo.

Galileo's principle of relativity : all inertial frames of reference are equal; the course of time, mass, acceleration and force are written in the same way .

One of the easiest physical phenomena is the mechanical movement of bodies. Who among you has not watched a car move, an airplane fly, people go, etc.! If, however, you are asked whether the building you are in is currently moving, you will probably answer that it is not. And you will be wrong!

Is the plane that you see in the sky moving now? If you are sure that he is moving, then again you are mistaken! But if you say that he is at rest, then in this case your answer will not be correct.

How to determine whether a particular body is moving or not? To do this, you must first understand what mechanical movement is.

Mechanical movement body is the process of changing its position relative to some other body chosen as the reference body.

Reference body- this is the body relative to which the position of other bodies is considered. The reference body is chosen arbitrarily. It can be anything: land, building, car, ship, etc.

To judge whether a body (for example, an airplane) is moving or not, you must first select a reference body, and then see if the position of the considered body changes relative to the selected reference body. In this case, the body can move relative to one reference body and at the same time not move relative to another reference body.

For example, a person sitting on a train moves relative to the canvas railway, but is at rest relative to the train car. A stone lying on the ground is at rest relative to the Earth, but moves (together with the Earth) relative to the Sun. The plane in the sky moves relative to the clouds, but is at rest relative to the pilot sitting in the seat.
That is why, without indicating the reference body, it is impossible to say whether the given body is moving or not. Without a reference body, any answer you give will be meaningless.

Is the building in which you are now at rest? The answer to this question depends on the choice of the reference body. If the reference body is the Earth, then yes, it is at rest. But if the reference body is a car passing by the building, then the building will move relative to it.

What role does body size play in describing its movement? In some cases, it is impossible to do without indicating the dimensions of the body and its parts. When, for example, a car enters a garage, the dimensions of the garage and the car will play a rather important role for its owner. But there are many situations where the size of the body is not important. If, for example, the same car is moving from Moscow to St. Petersburg and it is required to calculate the time of the car's movement, then we will not care what its dimensions are.

If the dimensions of the body are much smaller than the distances characteristic of the motion considered in the problem, then the dimensions of the body are neglected and the body is represented as material point. The word "material" emphasizes its difference from a geometric point. geometric point does not have any physical properties. A material point can have a mass, electric charge and some other characteristics.

In modern mechanics(theory of motion of bodies) material points are otherwise called particles. We will use both of these terms in what follows. Sometimes, speaking about the mechanical motion of particles, we will use the term "body", but we should not forget that this body is considered in such conditions when it can be taken as a material point.

Moving from one place to another, a particle (or material point) moves along a certain line. The line along which the particle moves is called trajectory.

trajectories can be different shape. It is sometimes possible to judge the shape of the trajectory by the visible trace left by the moving body. Such traces are sometimes left by flying planes or meteors sweeping through the night sky (Fig. 8). The shape of the trajectory depends on the choice of the reference body. For example, relative to the Earth, the trajectory of the Moon is a circle, and relative to the Sun - a line more complex shape(Fig. 9).
In what follows, we will consider the motion of all bodies (unless otherwise stated) relative to the Earth.

The trajectories of movement of different bodies can differ from each other not only in shape, but also in length.

The length of the trajectory along which the body moved is called the distance traveled. through.

In Figure 10, the dashed line shows the trajectory of a skier jumping from a springboard. The length of the trajectory OA is the path covered by the skier during the descent from the mountain.

When measuring a path, the unit of path is used. The unit of the path is the unit of length - meter(1m). In practice, other units of length are also used, for example:

1 km = 1000 m, 1 dm = 0.1 m, 1 cm = 0.01 m, 1 mm = 0.001 m.

1. What is mechanical movement? 2. What body is called the reference body? 3. Why is it necessary to indicate relative to which reference body the movement occurs? 4. In what cases can a body be considered as a material point? 5. What is another name for a material point? 6. What is a trajectory? 7. What is the difference between a path and a trajectory? 8. What actually moves: the Earth around the Sun or the Sun around the Earth? 9. Who is on the move: a passenger on the bus or a person standing at the bus stop? 10. Can the globe be considered a material point?

mechanical movement is a change that occurs over time relative position bodies in space.

An example is the movement Vehicle, aircraft and even fluctuations in the earth's crust.

Types of mechanical movement:

• translational mechanical movement;
• rotational mechanical movement;
• oscillatory mechanical movement.

In translational motion, all points of the body make the same movement. If you draw any straight line in the body during its movement, then it will remain parallel to itself. For example, such a movement occurs when using an elevator.
At rotary motion the points of the body will describe the circle. For example, a generator contains a rotor that describes a circle about the axis of this rotor.

Rotor

With oscillatory motion, the points of the body move, then up, then down. This type of movement can be considered on the example of usually a spring and a load. To do this, a load must be attached to the spring, and it will begin to oscillate.

Oscillatory motion on the example of a spring

Relativity of mechanical motion and the concept of a frame of reference

The concept of " relativity of mechanical motion” implies that a body can be at rest relative to some bodies, but move relative to other bodies. Because of this, it is important to indicate, by saying whether a body is moving or at rest, in relation to which state is being considered. For example, a boat is stationary relative to the water, but moving relative to the shore.

Therefore, it is necessary to indicate relative to which body the object is moving or at rest.

In different reference systems, the velocities of bodies will be different.

Reference system- this is a system that combines a body of reference, a reference associated with them and a device for measuring time.

1. Device for measuring time
2. Reference system
3. Reference body

For example, if a person moves in a train, then his speed will be different and will depend on the frame of reference with respect to which we will consider the movement, namely, on the frame of reference associated with the motionless Earth or on the frame of reference of the train.

It is worth noting that in different reference systems, the trajectories of the body's motion will also be different. An example is raindrops that fall vertically to the ground, and on the window of a speeding car they will leave a trail in the form of oblique jets.

The path in different reference systems will also be different. This can be seen in the example of a passenger who is sitting on a bus. So the path that he traveled relative to the bus during the trip is almost 0, but relative to the Earth he covered a relatively longer path.

A little about the relativity of speed

Let us assume that two bodies move in the same frame of reference with velocities V1 and V2. In this case, in order to find out the speed of the first body relative to the second, it is necessary to find the difference in speeds:

This is true only if the bodies are moving in the same direction, but when moving in the opposite direction, it is necessary to add the velocities

« Physics - Grade 10 "

According to the nature of the tasks to be solved, mechanics is divided into kinematics And dynamics.

In kinematics, the movement of bodies is described without clarifying the causes that cause this movement.

The first thing that catches your eye when observing the world around us is its variability. The world is not frozen, static. Changes in it are very diverse. But if you ask you what changes you notice most often, then the answer, perhaps, will be unequivocal: changes in the position of objects(or bodies, as physicists say) relative to the ground and relative to each other over time.

Whether a dog is running or a car is racing, the same process happens to them: their position relative to the ground and relative to you changes over time. They are moving. The spring is compressed, the board on which you sat down bends, the position changes various parts bodies relative to each other.

A change in the position of a body or body parts in space relative to other bodies over time is called mechanical movement.

The definition of mechanical motion looks simple, but this simplicity is deceptive. Read the definition again and think about whether all the words are clear to you: space, time, relative to other bodies. Most likely, these words require explanation.

Space and time.

Space and time are the most general concepts physics and... the least clear.

We do not have exhaustive information about space and time. But even the results that have been obtained today cannot be stated at the very beginning of the study of physics.

Usually it is enough for us to be able to measure the distance between two points in space with a ruler and time intervals with a clock. A ruler and a watch are the most important devices for measuring in mechanics, and even in everyday life. One has to deal with distances and time intervals in the study of many phenomena in all fields of science.

"...Regarding other bodies."

If this part of the definition of mechanical movement has escaped your attention, then you run the risk of not understanding the most important thing. For example, in the carriage compartment, there is an apple on the table. During the departure of the train, two observers (a passenger and a guide) are asked to answer the question: is the apple moving or not?

Each observer evaluates the position of the apple in relation to himself. The passenger sees that the apple is at a distance of 1 m from him and this distance is maintained over time. The person seeing off on the platform sees how, over time, the distance from him to the apple increases.

The passenger replies that the apple does not move mechanically - it is motionless; the guide says that the apple is moving.

The law of relativity of motion:
The nature of the movement of a body depends on the bodies with respect to which we consider this movement.

Let's start with the study of mechanical motion. It took mankind about two thousand years to embark on the right path, which ended with the discovery of the laws of mechanical motion.

The attempts of the ancient philosophers to explain the causes of motion, including mechanical motion, were the product of pure fantasy. Just as, they reasoned, a weary traveler speeds up his steps as he approaches home, so a falling stone begins to move faster and faster as it approaches mother earth. The movements of living organisms, such as cats, seemed at that time much simpler and more understandable than the fall of a stone. There were, however, brilliant insights. Thus, the Greek philosopher Anaxagoras said that the Moon, if it did not move, would fall to the Earth, as a stone falls from a sling.

However, the true development of the science of mechanical motion began with the works of the great Italian physicist G. Galileo.

Kinematics- This is a branch of mechanics that studies how to describe movements and the relationship between the quantities that characterize these movements.

To describe the movement of a body means to indicate a way to determine its position in space at any given time.

At first glance, the task of description seems very difficult. Indeed, look at swirling clouds, swaying leaves on a tree branch. Imagine the complex movement of the pistons of a car speeding down the highway. How to proceed to the description of the movement?

The simplest thing (and in physics they always go from simple to complex) is to learn how to describe the movement of a point. A point can be understood, for example, as a small mark made on a moving object - a soccer ball, a tractor wheel, etc. If we know how each such point moves (each very small plot) of the body, then we will know how the whole body moves.

However, when you say that you skied 10 km, then no one will specify which part of your body covered the distance of 10 km, although you are by no means the point. IN this case it doesn't matter in any significant way.

Let us introduce the concept of a material point - the first physical model of real bodies.

Material point- a body whose dimensions and shape can be neglected under the conditions of the problem under consideration.

Reference system.

The motion of any body, as we already know, is relative motion. This means that the motion of a given body can be different in relation to other bodies. When studying the motion of a body of interest to us, we must necessarily indicate with respect to which body this motion is being considered.

The body relative to which the motion is considered is called reference body.

To calculate the position of a point (body) relative to the selected reference body depending on time, one must not only associate a coordinate system with it, but also be able to measure time. Time is measured with a clock. Modern clocks are complex devices. They allow you to measure time in seconds with an accuracy of up to the thirteenth decimal place. Naturally, no mechanical watch can provide such accuracy. Thus, one of the most accurate mechanical clocks in the country on the Spasskaya Tower of the Kremlin is ten thousand times less accurate than the State standard of time. If the reference clock is not corrected, then by one second it will run away or lag behind in three hundred thousand years. It is clear that in everyday life there is no need to measure time with very high accuracy. But for physical research, astronautics, geodesy, radio astronomy, air traffic control high accuracy in the measurement of time is simply necessary. The accuracy with which we will be able to calculate the position of the body at any point in time depends on the accuracy of measuring time.

The totality of the reference body, the coordinate system associated with it and the clock is called reference system.

The figure shows the frame of reference chosen to consider the flight of a thrown ball. In this case, the reference body is the house, the coordinate axes are chosen so that the ball flies in the XOY plane, and a stopwatch is used to determine the time.

I propose a game: choose an object in the room and describe its location. Do this so that the guesser cannot make a mistake. Out? And what will come out of the description if other bodies are not used? The expressions will remain: "to the left of ...", "above ..." and the like. Body position can only be set relative to some other body.

Location of the treasure: "Stand at the eastern corner of the outermost house of the village, facing north, and after walking 120 steps, turn to face east and walk 200 steps. In this place, dig a hole of 10 cubits and you will find 100 bars of gold." It is impossible to find the treasure, otherwise it would have been dug up long ago. Why? The body in relation to which the description is made is not defined, it is not known in which village that house is located. It is necessary to accurately determine the body, which will be taken as the basis of our future description. Such a body in physics is called reference body. It can be chosen arbitrarily. For example, try choosing two different reference bodies and, relative to them, describe the location of the computer in the room. There will be two dissimilar descriptions.

Coordinate system

Let's look at the picture. Where is the tree, relative to cyclist I, cyclist II, and us looking at the monitor?

Relative to the reference body - cyclist I - the tree is on the right, relative to the reference body - cyclist II - the tree is on the left, relative to us it is in front. One and the same body - a tree, constantly in the same place, at the same time "to the left", and "to the right" and "in front". The problem is not only that different reference bodies are chosen. Consider its location relative to cyclist I.

In this picture, the tree on right from cyclist I

In this picture, the tree left from cyclist I

The tree and the cyclist did not change their location in space, but the tree can be "left" and "right" at the same time. In order to get rid of the ambiguity of the description of the direction itself, we will choose a certain direction as positive, the opposite of the chosen one will be negative. The selected direction is indicated by an axis with an arrow, the arrow indicates the positive direction. In our example, we choose and designate two directions. From left to right (the axis on which the cyclist moves), and from us inside the monitor to the tree, this is the second positive direction. If we denote the first direction we have chosen as X, the second as Y, we get a two-dimensional coordinate system.

Relative to us, the cyclist is moving in the negative direction on the x-axis, the tree is in the positive direction on the y-axis

Relative to us, the cyclist is moving in the positive direction on the x-axis, the tree is in the positive direction on the y-axis

Now determine which object in the room is 2 meters in the positive X direction (to your right), and 3 meters in the negative Y direction (behind you). (2;-3) - coordinates this body. The first digit "2" is used to indicate the location along the X axis, the second digit "-3" indicates the location along the Y axis. It is negative, because along the Y axis it is not in the side of the tree, but in opposite side. After the body of reference and direction is chosen, the location of any object will be described unambiguously. If you turn your back to the monitor, there will be another object to the right and behind you, but it will also have different coordinates (-2; 3). Thus, the coordinates accurately and unambiguously determine the location of the object.

The space in which we live is a space of three dimensions, as they say, a three-dimensional space. In addition to the fact that the body can be "right" ("left"), "in front" ("behind"), it can be even "above" or "below" you. This is the third direction - it is customary to designate it as the Z axis.

Is it possible to choose different axis directions? Can. But you can not change their direction during the solution of, for example, one problem. Is it possible to choose other axis names? It is possible, but you risk that others will not understand you, it is better not to do so. Is it possible to swap the x-axis with the y-axis? It is possible, but do not get confused in the coordinates: (x;y).

With a rectilinear motion of a body, one coordinate axis is sufficient to determine its position.

To describe motion on a plane, a rectangular coordinate system is used, consisting of two mutually perpendicular axes (Cartesian coordinate system).

Using a three-dimensional coordinate system, you can determine the position of the body in space.

Reference system

Each body at any moment of time occupies a certain position in space relative to other bodies. We already know how to determine its position. If over time the position of the body does not change, then it is at rest. If, over time, the position of the body changes, then this means that the body is moving. Everything in the world happens somewhere and sometime: in space (where?) and in time (when?). If we add to the body of reference, the coordinate system that determines the position of the body, a method of measuring time - hours, we get reference system. With which you can evaluate the movement or rest of the body.

Relativity of motion

The astronaut went into outer space. Is it at rest or in motion? If we consider it relative to the friend of the astronaut, who is nearby, he will rest. And if relative to an observer on Earth, the astronaut moves at great speed. Same with train travel. In relation to the people on the train, you sit still and read a book. But relative to the people who stayed at home, you are moving at the speed of a train.

Examples of choosing a reference body, relative to which in figure a) the train is moving (relative to trees), in figure b) the train is at rest relative to the boy.

Sitting in the car, waiting for departure. In the window we observe the train on a parallel track. When it starts to move, it is difficult to determine who is moving - our car or the train outside the window. In order to decide, it is necessary to assess whether we are moving relative to other stationary objects outside the window. We evaluate the state of our car in relation to different reference systems.

Changing displacement and speed in different reference systems

Displacement and speed change when moving from one frame of reference to another.

The speed of a person relative to the ground (fixed frame of reference) is different in the first and second cases.

Velocity addition rule: The speed of a body relative to a fixed frame of reference is 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.

Similar to the displacement vector. Movement addition rule: The movement of a body relative to a fixed frame of reference is the vector sum of the movement of a body relative to a moving frame of reference and the movement of a moving frame of reference relative to a fixed one.

Let a person walk along the car in the direction (or against) the movement of the train. Man is a body. The earth is a fixed frame of reference. The car is a moving frame of reference.

Changing the trajectory in different frames of reference

The trajectory of a body is relative. For example, consider the propeller of a helicopter descending to Earth. A point on the propeller describes a circle in the frame of reference associated with the helicopter. The trajectory of this point in the reference frame associated with the Earth is a helix.

translational movement

The movement of a body is a change in its position in space relative to other bodies over time. Each body has a certain size, sometimes different points of the body are in different places in space. How to determine the position of all points of the body?

BUT! Sometimes it is not necessary to specify the position of each point of the body. Let's consider such cases. For example, this does not need to be done when all points of the body move in the same way.

All the currents of the suitcase and the machine move in the same way.

The movement of a body in which all its points move in the same way is called progressive

Material point

It is not necessary to describe the movement of each point of the body even when its dimensions are very small compared to the distance it travels. For example, a ship crossing the ocean. Astronomers in describing the motion of the planets and celestial bodies relative to each other do not take into account their size and their own movement. Despite the fact that, for example, the Earth is huge, relative to the distance from the Sun, it is negligible.

There is no need to consider the movement of each point of the body when they do not affect the movement of the entire body. Such a body can be represented by a point. All the substance of the body, as it were, is concentrated into a point. We get a body model, without dimensions, but it has a mass. That's what it is material point.

One and the same body with some of its movements can be considered a material point, with others it cannot. For example, when a boy goes from home to school and at the same time travels a distance of 1 km, then in this movement he can be considered a material point. But when the same boy does exercises, then he can no longer be considered a point.

Consider moving athletes

In this case, the athlete can be modeled by a material point

In the case of an athlete jumping into the water (figure on the right), it is impossible to model it to the point, since the movement of the whole body depends on any position of the arms and legs

The main thing to remember

1) The position of the body in space is determined relative to the reference body;
2) It is necessary to set the axes (their directions), i.e. a coordinate system that defines the coordinates of the body;
3) The movement of the body is determined relative to the reference system;
4) In different reference systems, the speed of a body can be different;
5) What is a material point

More difficult situation addition of speeds. Have a person take a boat across a river. The boat is the investigated body. The fixed frame of reference is the earth. The moving frame of reference is a river.

The speed of the boat relative to the ground is the vector sum

What is the displacement of any point located on the edge of the disk with radius R when it is rotated by 600 relative to the stand? at 1800? Solve in reference systems associated with the stand and disk.

In the frame of reference associated with the stand, the displacements are equal to R and 2R. In the frame of reference associated with the disk, the displacement is zero all the time.

Why do raindrops in calm weather leave oblique straight stripes on the windows of a uniformly moving train?

In the reference frame associated with the Earth, the trajectory of the drop is a vertical line. In the frame of reference associated with the train, the movement of the drop on the glass is the result of the addition of two rectilinear and uniform movements: the train and the uniform fall of the drop in the air. Therefore, the trace of a drop on the glass is inclined.

How can you determine your running speed if you train on a treadmill with a broken automatic speed detection? After all, you can’t run a single meter relative to the walls of the hall.