Classification of motion in physics. Mechanical movement and its types

Mechanical movement are being considered for material point and For solid.

Motion of a material point

Forward movement an absolutely rigid body is a mechanical movement during which any straight line segment associated with this body is always parallel to itself at any time.

If you mentally connect any two points of a rigid body with a straight line, then the resulting segment will always be parallel to itself in the process of translational motion.

During translational motion, all points of the body move equally. That is, they travel the same distance in the same amount of time and move in the same direction.

Examples of translational motion: the movement of an elevator car, mechanical scales, a sled rushing down a mountain, bicycle pedals, a platform train, engine pistons relative to the cylinders.

Rotational movement

During rotational motion, all points physical body moving in circles. All these circles lie in planes parallel to each other. And the centers of rotation of all points are located on one fixed straight line, which is called axis of rotation. Circles described by points lie in parallel planes. And these planes are perpendicular to the axis of rotation.

Rotational movement occurs very often. Thus, the movement of points on the rim of a wheel is an example of rotational movement. Rotational motion is described by a fan propeller, etc.

Rotational motion is characterized by the following physical quantities: angular velocity rotation, rotation period, rotation frequency, linear speed points.

Angular velocity A body rotating uniformly is called a value equal to the ratio of the angle of rotation to the period of time during which this rotation occurred.

The time it takes a body to travel alone full turn, called rotation period (T).

The number of revolutions a body makes per unit time is called speed (f).

Rotation frequency and period are related to each other by the relation T = 1/f.

If a point is located at a distance R from the center of rotation, then its linear speed is determined by the formula:

Themes Unified State Exam codifier: mechanical motion and its types, relativity of mechanical motion, speed, acceleration.

The concept of movement is extremely general and covers the most wide circle phenomena. They study in physics different kinds movements. The simplest of these is mechanical movement. It is studied in mechanics.
Mechanical movement- this is a change in the position of a body (or its parts) in space relative to other bodies over time.

If body A changes its position relative to body B, then body B changes its position relative to body A. In other words, if body A moves relative to body B, then body B moves relative to body A. Mechanical motion is relative- to describe a movement, it is necessary to indicate in relation to which body it is being considered.

So, for example, we can talk about the movement of a train relative to the ground, a passenger relative to a train, a fly relative to a passenger, etc. Concepts absolute motion and absolute rest do not make sense: a passenger at rest relative to the train will move with it relative to the pillar on the road, perform a daily rotation with the Earth and move around the Sun.
The body relative to which motion is considered is called body of reference.

The main task of mechanics is to determine the position of a moving body at any time. To solve this problem, it is convenient to imagine the movement of a body as a change in the coordinates of its points over time. To measure coordinates, you need a coordinate system. To measure time you need a watch. All this together forms a frame of reference.

Frame of reference- this is a reference body together with a coordinate system and a clock rigidly connected to it (“frozen” into it).
The reference system is shown in Fig. 1. The movement of a point is considered in a coordinate system. The origin of coordinates is a body of reference.

Picture 1.

The vector is called radius vector dots The coordinates of a point are at the same time the coordinates of its radius vector.
The solution to the main problem of mechanics for a point is to find its coordinates as functions of time: .
In some cases, you can ignore the shape and size of the object being studied and consider it simply as a moving point.

Material point - this is a body whose dimensions can be neglected in the conditions of this problem.
Thus, a train can be considered a material point when it moves from Moscow to Saratov, but not when passengers board it. The Earth can be considered a material point when describing its movement around the Sun, but not its daily rotation around its own axis.

The characteristics of mechanical motion include trajectory, path, displacement, speed and acceleration.

Trajectory, path, movement.

In what follows, when speaking about a moving (or at rest) body, we always assume that the body can be taken as a material point. Cases when idealization of a material point cannot be used will be specially discussed.

Trajectory - this is the line along which the body moves. In Fig. 1, the trajectory of a point is a blue arc, which the end of the radius vector describes in space.
Path - this is the length of the trajectory section traversed by the body in a given period of time.
Moving is a vector connecting the initial and final position of the body.
Let us assume that the body began to move at a point and ended its movement at a point (Fig. 2). Then the path traveled by the body is the trajectory length. The displacement of a body is a vector.

Figure 2.

Speed ​​and acceleration.

Consider the movement of a body in rectangular system coordinates with the basis (Fig. 3).

Figure 3.

Let at the moment of time the body be at a point with the radius vector

After a short period of time the body found itself at a point with
radius vector

Body movement:

(1)

Instantaneous speed at a moment in time - this is the limit of the ratio of movement to the time interval, when the value of this interval tends to zero; in other words, the speed of a point is the derivative of its radius vector:

From (2) and (1) we obtain:

The coefficients of the basis vectors in the limit give the derivatives:

(The derivative with respect to time is traditionally denoted by a dot above the letter.) So,

We see that the projections of the velocity vector onto coordinate axes are derivatives of the coordinates of the point:

When it approaches zero, the point approaches the point and the displacement vector turns in the direction of the tangent. It turns out that in the limit the vector is directed exactly tangent to the trajectory at point . This is shown in Fig. 3.

The concept of acceleration is introduced in a similar way. Let the speed of the body be equal at the moment of time, and after a short interval the speed becomes equal.
Acceleration - this is the limit of the ratio of the change in speed to the interval when this interval tends to zero; in other words, acceleration is the derivative of speed:

Acceleration is thus the “rate of change of velocity.” We have:

Consequently, acceleration projections are derivatives of velocity projections (and, therefore, second derivatives of coordinates):

The law of addition of speeds.

Let there be two reference systems. One of them is related to motionless body countdown We will denote this reference system and call it motionless.
The second reference system, denoted by , is associated with a reference body that moves relative to the body with a speed of . We call this reference system moving . Additionally, we assume that the coordinate axes of the system move parallel to themselves (there is no rotation of the coordinate system), so that the vector can be considered the speed of the moving system relative to the stationary one.

A fixed frame of reference is usually associated with the earth. If a train moves smoothly along the rails with a speed, this frame of reference associated with the train car will be a moving frame of reference.

Note that the speed any points of the car (except for the rotating wheels!) is equal to . If a fly sits motionless at some point in the carriage, then relative to the ground the fly moves at a speed of . The fly is carried by the carriage, and therefore the speed of the moving system relative to the stationary one is called portable speed .

Now suppose that a fly crawled along the carriage. The speed of the fly relative to the car (that is, in a moving system) is designated and called relative speed. The speed of a fly relative to the ground (that is, in a stationary frame) is denoted and called absolute speed .

Let's find out how these three speeds are related to each other - absolute, relative and portable.
In Fig. 4 fly is indicated by a dot. Next:
- radius vector of a point in a fixed system;
- radius vector of a point in a moving system;
- radius vector of the body of reference in a stationary system.

Figure 4.

As can be seen from the figure,

Differentiating this equality, we get:

(3)

(the derivative of a sum is equal to the sum of derivatives not only for the case scalar functions, but also for vectors).
The derivative is the speed of a point in the system, that is, the absolute speed:

Similarly, the derivative is the speed of a point in the system, that is, the relative speed:

What is it? This is the speed of a point in a stationary system, that is, the portable speed of a moving system relative to a stationary one:

As a result, from (3) we obtain:

Law of addition of speeds. The speed of a point relative to a stationary reference frame is equal to the vector sum of the speed of the moving system and the speed of the point relative to the moving system. In other words, absolute speed is the sum of portable and relative speeds.

Thus, if a fly crawls along a moving carriage, then the speed of the fly relative to the ground is equal to the vector sum of the speed of the carriage and the speed of the fly relative to the carriage. Intuitively obvious result!

Types of mechanical movement.

The simplest types of mechanical motion of a material point are uniform and rectilinear motion.
The movement is called uniform, if the magnitude of the velocity vector remains constant (the direction of the velocity may change).

The movement is called straightforward , if the direction of the velocity vector remains constant (and the magnitude of the velocity may change). The trajectory of rectilinear motion is a straight line on which the velocity vector lies.
For example, a car that is traveling with constant speed along a winding road, makes a uniform (but not rectilinear) movement. A car accelerating on a straight section of highway moves in a straight line (but not uniformly).

But if, when moving a body, both the velocity module and its direction remain constant, then the movement is called uniform rectilinear.

In terms of the velocity vector, one can give more short definitions to these types of movement:

The most important special case uneven movement is uniformly accelerated motion, at which they remain constant module and direction of the acceleration vector:

Along with the material point, mechanics considers another idealization - a rigid body.
Solid - This is a system of material points, the distances between which do not change over time. The rigid body model is used in cases where we cannot neglect the dimensions of the body, but can ignore change size and shape of the body during movement.

The simplest types of mechanical motion of a solid body are translational and rotational motion.
The movement of the body is called progressive, if any straight line connecting any two points of the body moves parallel to its original direction. During translational motion, the trajectories of all points of the body are identical: they are obtained from each other by a parallel shift (Fig. 5).

Figure 5.

The movement of the body is called rotational , if all its points describe circles lying in parallel planes. In this case, the centers of these circles lie on one straight line, which is perpendicular to all these planes and is called axis of rotation.

In Fig. 6 shows a ball rotating around vertical axis. This is how they usually draw Earth in corresponding problems of dynamics.

Figure 6.

Mechanical movement of a body (point) is the change in its position in space relative to other bodies over time.

Types of movements:

A) Uniform straight motion material point: Initial conditions

. Initial conditions

G) Harmonic oscillatory motion. An important case of mechanical motion is oscillations, in which the parameters of a point’s motion (coordinates, speed, acceleration) are repeated at certain intervals.

ABOUT scriptures of the movement . There are various ways to describe the movement of bodies. With the coordinate method specifying the position of a body in a Cartesian coordinate system, the movement of a material point is determined by three functions expressing the dependence of coordinates on time:

x= x(t), y=y(t) And z= z(t) .

This dependence of coordinates on time is called the law of motion (or equation of motion).

With the vector method the position of a point in space is determined at any time by the radius vector r= r(t) , drawn from the origin to a point.

There is another way to determine the position of a material point in space for a given trajectory of its movement: using a curvilinear coordinate l(t) .

All three methods of describing the motion of a material point are equivalent; the choice of any of them is determined by considerations of the simplicity of the resulting equations of motion and the clarity of the description.

Under reference system understand a reference body, which is conventionally considered motionless, a coordinate system associated with the reference body, and a clock, also associated with the reference body. In kinematics, the reference system is selected in accordance with the specific conditions of the problem of describing the motion of a body.

2. Trajectory of movement. Distance traveled. Kinematic law of motion.

The line along which a certain point of the body moves is called trajectorymovement this point.

The length of the trajectory section traversed by a point during its movement is called the path traveled .

The change in radius vector over time is called kinematic law :
In this case, the coordinates of the points will be coordinates in time: x= x(t), y= y(t) Andz= z(t).

In curvilinear motion, the path is greater than the displacement modulus, since the length of the arc is always greater than the length of the chord contracting it

Vector drawn from initial position moving point to its position at a given time (increment of the radius vector of the point over the considered period of time), is called moving. The resulting displacement is equal to the vector sum of successive displacements.

During rectilinear movement, the displacement vector coincides with the corresponding section of the trajectory, and the displacement module is equal to the distance traveled.

3. Speed. Average speed. Velocity projections.

Speed - speed of coordinate changes. When a body (material point) moves, we are interested not only in its position in the chosen reference system, but also in the law of motion, i.e., the dependence of the radius vector on time. Let the moment in time corresponds to the radius vector a moving point, and a close moment in time - radius vector . Then in a short period of time
the point will make a small displacement equal to

To characterize the movement of a body, the concept is introduced average speed his movements:
This quantity is a vector quantity, coinciding in direction with the vector
. With unlimited reduction Δt the average speed tends to a limiting value called instantaneous speed :

Velocity projections.

A) Uniform linear motion of a material point:
Initial conditions

B) Uniformly accelerated linear motion of a material point:
. Initial conditions

B) Movement of a body along a circular arc with a constant absolute speed:

Mechanical movement A body is called a change in its position in space relative to other bodies over time. For example, a person riding an escalator in the subway is at rest relative to the escalator itself and is moving relative to the walls of the tunnel

Types of mechanical movement:

• rectilinear and curvilinear - according to the shape of the trajectory;
• uniform and uneven - according to the law of motion.

Mechanical movement relatively. This is manifested in the fact that the shape of the trajectory, displacement, speed and other characteristics of the body’s movement depend on the choice of the reference system.

The body relative to which motion is considered is called reference body. The coordinate system, the reference body with which it is associated, and the device for counting time form reference system , relative to which the movement of the body is considered.

Sometimes the size of the body compared to the distance to it can be neglected. In these cases, the body is considered material point.

Determining the position of the body at any time is the main task of mechanics.

Important characteristics of movement are trajectory of a material point, displacement, speed and acceleration. The line along which it moves material point, called trajectory . The length of the trajectory is called path (L). The unit of measurement for the path is 1m. The vector connecting the initial and end point trajectory is called displacement (). Displacement unit-1 m.

The simplest type of motion is uniform linear motion. A movement in which a body makes the same movements at any equal intervals of time is called rectilinear uniform movement. Speed() - vector physical quantity, characterizing the speed of movement of the body, numerically equal to the ratio movements over a short period of time to the value of this interval. The defining formula for speed has the form v = s/t. Speed ​​unit - m/s. Speed ​​is measured with a speedometer.

The movement of a body in which its speed changes equally over any period of time is called uniformly accelerated or equally variable.

— a physical quantity that characterizes the rate of change in speed and is numerically equal to the ratio of the vector of change in speed per unit time. SI unit of acceleration — m/s 2 .

uniformly accelerated, if the speed module increases.—condition uniformly accelerated motion. For example, accelerating vehicles - cars, trains and free fall bodies near the Earth's surface ( = ).

Equally alternating motion called equally slow, if the speed module decreases. — condition of uniformly slow motion.

Instantaneous speed uniformly accelerated linear motion

MINISTRY OF EDUCATION AND SCIENCE OF UKRAINE

Kyiv NATIONAL TECHNICAL UNIVERSITY

(Kyiv POLYTECHNIC INSTITUTE)

FACULTY OF PHYSICS

ABSTRACT

ON THE TOPIC OF: Mechanical movement

Completed by: 4th year student

Group 105 A

Zapevailova Diana

§ 1. Mechanical motion

When a ball or cart placed on a table changes its position relative to the table, we say that it is moving. In the same way, we say that a car is moving if it changes its position in relation to the road.

Changing the position of a given body in relation to some other bodies is called mechanical motion.

In cosmic space, mechanical movements are performed by the Earth, the Moon and other planets, comets, the Sun, stars, and nebulae. On Earth we observe the mechanical movements of clouds, water in rivers and oceans, animals and birds; Mechanical movements are also performed by man-made ships, cars, trains and airplanes; parts of machines, machine tools and devices; bullets, shells, bombs and mines, etc., etc.

The branch of physics called mechanics deals with the study of mechanical movements. The word "mechanics" comes from Greek word“mechanz”, which means machine, device. It is known that already the ancient Egyptians, and then the Greeks, Romans and other peoples built various machines that were used for transport, construction and military affairs (Fig. 1); during the operation of these machines there was movement (movement) in them various parts: levers, wheels, weights, etc. The study of the movement of parts of these machines led to the creation of the science of the movements of bodies - mechanics.

The movement of a given body can be of a completely different nature depending on in relation to which bodies a change in its position is observed.

For example, an apple lying on the table of a moving carriage is at rest in relation to the table and all other objects in the carriage; but it is in motion in relation to objects located on the ground, outside the train car. In calm weather, streams of rain appear vertical if you watch them from the window of a carriage standing at the station; In this case, the drops leave vertical marks on the window glass. But in relation to a moving carriage, the streams of rain will appear oblique: raindrops will leave inclined marks on the glass, and the greater the speed of the carriage, the greater the slope.

The dependence of the nature of movement on the choice of bodies to which the movement relates is called the relativity of movement. All movement and, in particular, rest are relative.

Thus, in answering the question whether a body is at rest or moving and how it moves, we must indicate in relation to which bodies the movement of the body of interest to us is considered. In cases where this is not explicitly stated, we always mean such bodies. Thus, when we simply speak of the falling of a stone, the movement of a car or an airplane, we always mean that we are talking about movement in relation to the Earth; When we talk about the movement of the Earth as a whole, we usually mean movement relative to the Sun or stars, etc.

When starting to study the movement of individual bodies, we may not first ask ourselves the question of the reasons that cause these movements. For example, we can follow the movement of a cloud without paying any attention to the wind that drives it; we see a car moving on the highway, and while describing its movement, we can not pay attention to the operation of its engine.

The department of mechanics in which movements are described and studied without investigating the causes that cause them is called kinematics.

To describe the movement of a body, it is necessary, generally speaking, to indicate how the position of various points of the body changes with time. When a body moves, each point of it describes a certain line, which is called the trajectory of this point.

By running chalk along the board, we leave a mark on it - the trajectory of the tip of the chalk relative to the board. The luminous trail of a meteor represents the trajectory of its movement (Fig. 2). The luminous trace of the tracer bullet shows the shooter its trajectory and makes it easier to zero in (Fig. 3).

The trajectories of movement of different points of the body can, generally speaking, be completely different. This can be shown, for example, by quickly moving an archer smoldering at both ends in a dark room. Thanks to the ability of the eye to retain visual impressions, we will see the trajectories of the smoldering ends and can easily compare both trajectories (Fig. 4).

So, the trajectories of different points of a moving body can be different. Therefore, to describe the movement of a body, it is necessary to indicate how its various points move. Having indicated, for example, that one end of a splinter moves in a straight line, we will not give a complete description of the movement, because it is not yet known how its other points, for example, the second end of the splinter, move.

The simplest is the movement of a body in which all its POINTS move the same way - they describe the same trajectories. This movement is called translational. It's easy to replicate this type of movement.

We will move our splinter so that it remains parallel to itself all the time.

We will see that its ends will describe identical trajectories. These can be straight or curved lines (Fig. 5). It can be proven that in forward motion any Pa straight line drawn in the body remains parallel to itself.

It is convenient to use this feature to answer the question of whether the movement of a given body is translational. For example, when rolling a cylinder along inclined plane straight lines intersecting the axis do not remain parallel to themselves, therefore, the rolling of the cylinder is not forward motion(Fig. 6, A). But when sliding along the plane of a block with flat edges, any straight line drawn in it will remain parallel to itself - sliding of the block is a translational movement (Fig. 6, b). Translational motion is the movement of a needle in a sewing machine, the movement of a piston in a steam engine cylinder or in a motor cylinder, the movement of a nail hammered into a wall, the movement of ferris wheel booths (Fig. 141 on p. 142). Approximately translational is the movement of a file during filing plane (Fig. 7), movement of the car body (but not the wheels!) when driving in a straight line, etc.

Another common type of movement is rotational movement of the body. During rotational movement everything points of the body describe circles whose centers lie on a straight line(straight 00", rice. 8), called the axis of rotation. These circles are located in parallel planes perpendicular to the axis of rotation. The axis points remain stationary. Any straight line passing at an angle to the axis of rotation does not remain parallel to itself during movement. Thus, rotation is not a translational motion. Rotational motion is very widely used in technology; the movements of wheels, blocks, shafts and axes of various mechanisms, propellers, etc. are examples of rotational motion. The daily movement of the Earth is also a rotational movement.

We have seen that in order to describe the movement of a body it is necessary, generally speaking, to know how various points of the body move. But if a body moves translationally, then all its points move equally. Therefore, to describe the translational motion of a body, it is enough to describe the movement of any one point of the body. For example, when describing the forward motion of a car, it is enough to indicate how the end of the flag on the radiator or any other point on its body moves.

Thus, in a number of cases, the description of the movement of a body is reduced to the description of the movement of a point. Therefore, we will begin the study of movements by studying the movement of a single point.

The movements of a point, first of all, differ in the type of trajectory it describes. If the trajectory that a point describes is a straight line, then its movement is called rectilinear. If the trajectory of movement is a curve, then the movement is called curvilinear.

Since different points bodies can move in different ways, the concept of rectilinear (or curvilinear) motion refers to the movement of individual points, and not the entire body as a whole. Thus, the rectilinearity of the movement of one or several points of the body does not at all mean the rectilinear movement of all other points of the body. For example, when rolling a cylinder (Fig. 6, A) all points lying on the cylinder axis move rectilinearly, while other points of the cylinder describe curved trajectories. Only with the translational movement of a body, when all its points move equally, can we talk about the rectilinearity of the movement of the body as a whole and, in general, about the trajectory of the entire body.

The description of the movement of one point of the body can often be limited to the case when the body performs translational and rotational motion, if the distance to the axis of rotation is very large compared to the size of the body. This is, for example, the movement of an airplane describing a turn, or the movement of a train on a curved track, or the movement of the Moon relative to the Earth. In this case, the circles described by different points of the body differ very little from each other. The trajectories of movement of these points turn out to be almost identical, and if we are not interested in the rotation of the body as a whole, then to describe the movement of its points it is also sufficient to indicate how any one point of the body moves.

The description of the movement of the body should make it possible to determine the position of the body at any time. What do we need to know for this?

Let's say that we want to determine the position that a moving train occupies at a certain moment in time. To do this we need to know the following:

The trajectory of the train. If, for example, the train is coming from Moscow to Leningrad, then railway track Moscow-Leningrad represents this trajectory.

The position of the train on this trajectory at any particular point in time. For example, it is known that at 0:30 am the train left Moscow. In our problem, Moscow is the initial position of the train, or the beginning of the track counting, and, accordingly, 0h. 30 m is the initial moment, or the beginning of the countdown.

The period of time that separates the moment of time we are interested in from the initial one. Let this interval be 5 hours, i.e. we are looking for the position of the train at 5:30 am.

4) The distance traveled by the train during this period of time. Let's say this path is 330 km.

Based on this data, we can answer the question that interests us. Taking the map (Fig. 9) and placing it along the line depicting the Moscow-Leningrad road, a distance of 330 km from. Moscow towards Leningrad, we will find that at 5:30 am the train was at Bologoye station.

The beginning of the path and the beginning of the time do not necessarily coincide with the beginning of the movement in question. The starting moment and this moment and this position are called the initial position not because they correspond to the beginning of the movement, but because they are the initial (initial) data of our task. As initial data, you can specify the position of the train at any specific point in time. It would be enough, for example, to indicate that, Suppose, at 1:15 a.m. the train passed by the Kryukovo station. Then the Kryukovo station would be the beginning of the countdown of the route, and 1 hour 15 m, night - the beginning of the countdown of time. The moment of time that interests us (5:30 a.m.) is separated from the initial moment by an interval of 4:15 a.m.; if we know that in 4 hours 15 minutes the train traveled 290 km, then we will find, just like in the first case, that at 5:30 am the train will be at Bologoye station (Fig. 9).

So, to describe the movement, it is necessary to know the trajectory of the body, establish the position of the body on the trajectory in various moments time and determine the length of the path traveled by the body over certain periods of time. But in order to determine the path traversed by a body over a given period of time, we must be able to measure these quantities - the length of the path and the period of time. Thus, any description of motion is based on measurements of length and time intervals.

In what follows, we will denote the length of the path traveled by a body over a certain period of time, in other words, the movement of the body, by the letter 5, and the length of the time interval by the letter t. In this case, next to the letters we will sometimes put the designation of those units in which a given quantity is measured. For example, S M, tsec will mean that we measured the length of the path in meters, and the period of time in seconds.

The basic unit of measurement for path length (as well as length in general) is the meter. The distance between two lines on a platinum-iridium rod stored at the International Bureau of Weights and Measures in Paris was taken as a sample meter (Fig. 10). In addition to this basic unit, other units are used in physics - multiples of the meter and fractions of a meter:

The vernier is an additional scale that can move along the main one. The vernier divisions are less than the main scale divisions by 0.1 of their value (for example, if the main scale divisions are equal to 1 mm, then the vernier divisions are 0.9 mm). The figure shows that the length of the measured body L more than 3 mm, but less than 4 mm. To find how many tenths of a millimeter is the excess length versus 3 mm, look at which of the vernier strokes coincides with any of the main scale strokes. In our figure, the seventh line of the vernier coincides with the tenth line of the main scale. This means that the sixth stroke of the vernier deviates from the ninth stroke of the main scale by 0.1 mm, fifth from eighth - by 0.2 mm etc.; initial from the third - by 0.7 mm. It follows that the length of the object A equal to as many whole millimeters as there are before the beginning of the vernier (3 mm), and as many tenths of a millimeter as the number of nonius divisions located from the beginning to the matching strokes (0.7 mm). So, the length of the object L equal to 3.7 mm.

1 kilometer (1000 meters), 1 centimeter (1/100 meter), 1 millimeter (1/1000 meter), 1 micron (1/1000000 meter, denoted mk or - greek letter"mu")

In practice, copies of this meter are used to measure length, i.e. wires, rods, rulers or tapes with divisions, the length of which is equal to the length of the standard meter or part thereof (centimeters and millimeters). When measuring, one end of the length being measured is aligned with the beginning of the measuring ruler and the position of the second end is marked on it. For more accurate readings, auxiliary devices are used. One of them - n he i-u s - is shown in Fig. 11. Fig. 12 shows a running measuring device - a caliper) equipped with a vernier.

Since 1963, the USSR has adopted the SI system of units (from the words “International System”) as recommended in all fields of science and technology. According to this system, a meter is defined as a length equal to 1650763.73 wavelengths of red light emitted by a special lamp in which the luminous substance is krypton gas. In practice, this unit of length is the same as the Parisian meter model, but it can be reproduced optically with greater accuracy than the model. called a change in the position of an object... . The simplest object to study mechanical movement can serve as a material point-body... .... tn), is called a trajectory movement. At movement point is the end of its radius vector...