The main sign of an absolutely solid body. The concept of absolutely solid and the laws of rotational motion

Subject of physics

1.1. Matter as an object of knowledge

Physics is a science of the most common properties and forms of motion of matter. Physical forms of motion of matter (mechanical, thermal, electromagnetic, etc.) take place in the "inanimate" nature, but they are the components of the more complex forms of movement relating to the world of "living" matter.

Matter is an objective reality, which is given to a person in his feelings, existing independently of his consciousness and sensations. The individual properties of matter can be copied, being photographed, measured by human senses and special devices created by it. It follows from this that the matter is known.

Physics - Science, which is continuously developing, as well as every other science, because The wider circle of knowledge, the greater the perimeter of the borders with the unknown.

Communication with philosophy:

Academician S.I.Vavilov noted in one of his articles: "... The maximum community of a significant part of the content of physics, its factors and laws of invoice has brought physics with philosophy ... Sometimes physical statements in their nature are such that they are difficult to distinguish them from philosophical statements, and the physicist must be a philosopher."

The justice of this statement confirms the facts of the history of the development of science. Such, for example, as attempts to invent an eternal engine, inexhaustible energy sources, attempts to find the smallest particle of substance. And such at first they considered a molecule, then the atom, then the electron.

And only an armed with knowledge of philosophy naturalist knows that there can be no eternal engine, which is not the smallest indivisible particle of matter, as not and the largest - the universe is infinite. It is difficult to imagine the uninitiated person, but it is so, and physics and philosophy agree.

Currently known two types of material existence: substance and field.

To the first kind of matter - substance - These are, for example, atoms, molecules and all bodies built ones.

The second type of matter forms magnetic, electric, gravitational other fields.

And if the substance is able to reflect in human sensation organs we do not see the field And do not feel. This does not mean that there are no fields. A person can detect the presence of fields indirectly. The fact that the magnetic field is logically easy to make sure, looking, for example, to the operation of magnetic cranes, electrical machines. You can take two magnets and try to connect them to the poles of the same name, and make sure that it is impossible. You will not see any substance between the poles, but the invisible forces prevent the connection of the magnets of the same names in the same way as the poles are attracted. These experiments convince: the field is financially.

Different types of matter can turn into each other. So, for example, an electron and a positron, which are a substance, can turn into photons, i.e. In the electromagnetic field. Reverse process is possible.

Matter is in continuous movement. No movement - no matter. Movement - an integral property of matter which is indisposed and unable, like the matter itself.

Matter exists and moves in space and timewhich are forms of existence of matter.

1.2. Methods physical research

French materialist-enlightener Denis Didro in the work "Thought to explain nature" so characterized the path of scientific knowledge: "We have three main research facilities: observation Nature. Reflection and experiment.

Observation collects facts ; reflection by them combines ; experience checking Result of combinations. Needless diligence To observe nature, depth For thinking I. accuracy For experience. "

Physical laws are established on the basis of summarizing experienced facts and express objective patterns existing in nature. The main methods of physical research are

– experience,

– hypothesis,

– experiment,

– theory .

Found laws are usually formulated in the form of quantitative relations between different physical quantities.

Experience or experiment It is the main research method in physics. Hypotheses are attracted to explain the experimental data.

Hypothesis- Scientific assumption put forward to explain any fact or phenomenon. After checking and confirmation hypothesis becomes scientific theory or law.

Physical laws – sustainable repeating objective patterns that exist in nature.

Physical theory It is a system of basic ideas that summarize experienced data and reflecting objective patterns of nature.

Science arose in ancient times as an attempt to comprehend the surrounding phenomena, the relationship between nature and man. At first she was not divided into separate directions, as now, and united in one common science - philosophy. Astronomy was separated into separate discipline ahead of physics and is along with mathematics and mechanics of one of ancient Sciences. Later, the science of nature also stand out in an independent discipline. Ancient Greek scientist and philosopher Aristotle called one of his writings with physics.

One of the main tasks of physics is to explain the structure of the world around us and the processes occurring in it, to understand the nature of the observed phenomena. Another important task is to identify and know the laws that obeys the world. Knowing the world, people use the laws of nature. All modern techniques are based on the application of laws discovered by scientists.

In the invention in the 1780s. The steam engine began an industrial revolution. The first steam engine invented the English scientist Thomas Newkun in 1712. The steam machine is suitable for use in the amendment, first created in 1766 by the Russian inventor Ivan Solvunov (1728-1766). Shoulder James WATT improved the design. Created by him in 1782. The two-stroke steam engine led the machine and mechanisms in the factory.

The power of the couple led the pumps, trains, steamers, spinning machines and many other machines. A powerful impetus for the development of equipment was the creation of an English physicist "ingenious self-taught" Michael Faraday in 1821 of the first electric motor. Creation in 1876. The German engineer Nicholas OTTO has opened the era of the automotive industry, made a possible existence of cars, diesel locomotives, vessels and other technical objects possible.

What was previously considered fiction now becomes real lifewhich we no longer imagine without audio and video equipment, personal computer, cell phone and internet. Their occurrence is required to discover made in various fields of physics.

However, the development of technology contributes to progress in science. The creation of an electron microscope made it possible to look inside the substance. Creating accurate measuring instruments made it possible a more accurate analysis of the results of experiments. A huge breakthrough in the field of space study was associated with the emergence of new modern devices and technical devices.

Thus, physics as science plays a huge role in the development of civilization. She turned over the most fundamental ideas of people - ideas about space, time, the device of the universe, allowing humanity to make a qualitative leap in its development. The successes of physics allowed to make a number of fundamental discoveries in other natural sciences, in particular, in biology. The development of physics to the greatest extent ensured the rapid progress of medicine.

With the successes of physics, both the hopes of scientists are connected to the provision of humanity with inexhaustible alternative energy sources, the use of which will solve many serious environmental problems. Modern physics is designed to ensure an understanding of the most depths of the foundations of the universe, the emergence and development of our universe, the future of human civilization.

The history of the development of biophysics

The development and formation of biophysics as border science took place a number of stages. Already at the initial stages, biophysics was closely related to the ideas and methods of physics, chemistry, physical chemistry and mathematics.

Penetration and application of the laws of physics to describe various patterns of wildlife met a number of difficulties.

The subject of biophysics is the study of physical and physicochemical processes underlying life. By the nature of the objects of research, biophysics is typical biological science, and according to the study and analysis methods, the research results is a kind of selection of physics. Biophysical methods are created on the basis of physical and physicochemical methods of studying nature. In these methods, difficult qualities must be combined.
1. High sensitivity.
2. Great accuracy.
These requirements are not satisfying any methods, however, the most widespread use of the following methods for biophysical studies:
- optical;
- Radio spectroscopy.
- ultrasound radiooscopy;
- electron-paramagnetic resonance spectroscopy (EPR);
- Nuclear magnetic resonant spectroscopy.
It should be noted that any studies require that the recording devices do not make distortions into the studied process, however, it is difficult to compare any physical system with a living organism for the extraordinarily high sensitivity of the body to any impacts on it. Impacts do not simply violate the normal course of biological processes, but cause complex adaptive reactions, a variety of swollen organs and in various conditions. The distortion of the meaning of measurements may be so significant that it becomes impossible to amend the phenomenon that is not characteristic of the object being studied. At the same time, the correction methods used with success in physics and technique are often useless in biophysics.

In the last century, attempts to use the methods and theory of physics to explore and understand the nature of biological phenomena were made to explore and understand the nature of biological phenomena. Moreover, the researchers considered living fabrics and cells as physical systems and did not take into account the fact that chemistry plays the main role in these systems. That is why attempts to solve the tasks of evaluating the properties of a biological object with a purely physical position were naive.

The main method of this direction was the search for analogy.

Biological phenomena, similar to purely physical phenomena, were interpreted, respectively, as physical.

For example, the effect of muscle reduction was explained by analogy with a piezoelectric effect, on the basis of only the fact that when the potential is applied to the crystal, a change in the length of the crystal occurred, as well as the change in the length of the muscle during the reduction. Cell growth was considered a similar crystal growth. Cellular division was considered as a phenomenon due to only the surfactant properties of the outer layers of protoplasm. The amoeboid motion of the cells was likened to change surface tension And, accordingly, it was simulated by the movement of mercury drops in the acid solution.

Even much later, in the twenties of our century, we considered in detail and studied the model of nervous on the analysis of the behavior of the so-called model Lily. This model was an iron wire that immersed in an acid solution and covered with an oxide film. When applied to the surface scratches, the oxide was destroyed, and then restored, but at the same time collapsed in the neighboring plot and so on. In other words, it turned out the distribution of the wave of destruction and recovery, very similar to the distribution of electronegability wave arising during nerve irritation.

The emergence and development in the physics of quantum theory led to an attempt to explain the effect of radiant energy on biological objects from the position of statistical physics. At this time, a formal theory appears, which explained the radial defeat as the result of the random quantum (or nuclear particle) in particularly vulnerable cellular structures. At the same time, those specific photochemical reactions and subsequent chemical processes were completely overlooked from the form, which determine the development of radiation lesion over time.

Relatively recently, on the basis of the formal similarity of the patterns of electrical conductivity of live tissues and electrical conductivity of semiconductors, semiconductors tried to apply the theory of semiconductors to explain the structural features of the entire cells.

This direction based on models and analogies, although it can attract a very perfect mathematical apparatus to work, is unlikely to bring biologists to understand the essence of biological processes. Attempts to use purely physical ideas to understand the biological phenomena and nature of living matter gave a large number of speculative theories and clearly showed that the direct path of physics into biology is not productive, since living organisms are incomparably closer to chemical systemsthan to physical.

Significantly more fruitful was the introduction of physics in chemistry. The use of physical ideas has played a major role in the understanding of the mechanisms of chemical processes. The emergence of physical chemistry played a revolutionary role. Based on the close contact of physics and chemistry, modern chemical kinetics and chemistry of polymers have arisen. Some sections of physical chemistry in which physics gained dominant value was called chemical physics.

It is with the emergence of physical chemistry that the development of biophysics is connected.

Many of the important ideas for the biology came to it from physical chemistry. It is enough to recall that the use of the physicochemical theory of electrolyte solutions to biological processes has led to the idea of \u200b\u200ban important role of ions in the basic processes of life.

With the development of physical and colloidal chemistry, the front of work in the field of biophysics is expanding. Attempts appear to explain from these positions the mechanisms of response of the body to external influences. A larger role in the development of biophysics was played by the Loeb School (J. LoEB 1906 g). In the work of Loe, the physico-chemical bases of parthenogenesis phenomena and fertilization were identified. Specific physico-chemical interpretation was obtained by the phenomenon of antagonism of ions.

Later, classical studies have appeared on the role of ionic and colloid processes in inflammation pathology. These studies are completed by the fundamental work " Physical chemistry In internal medicine, "which is published in Russia in 1911-1912.

First world War Suspended the development of biophysics as science.

But in 1922, the "Institute of Biophysics" opens in the USSR, which manages P.P. Lazarev. Here he is developing an ionic theory of excitement, which at the same time is being developed and the nonston was found that in the phenomena of excitement and the decisive role belongs to the ions.

S.I. Vavilov deals with the limit sensitivity of the eye. V.Yu. CHAVEN is developing the ionic theory of the occurrence of biopotentials, N.K. Koltsov justifies the role of surface tension, ions and pH in morphogenesis.

The Koltsova School played a prominent role in the development of biophysics in the USSR. His disciples widely developed issues of influence of physicochemical factors external environment on cells and their structures.

Somewhat later (1934) Rodionov S.R. And Frank G.M. Opened the phenomenon of photoreactivation, the headset (1944) method of electron paramagnetic resonance.

The main result of the initial period of development of biophysics is the conclusion about the principal possibility of using the biology of the basic laws of physics as a fundamental natural Science On the laws of motion of matter.

Important general scientific importance for the development of various areas of biology have the experimental evidence of the law of energy conservation law (the first law of thermodynamics) obtained during this period

The use of presentations of colloid chemistry to the analysis of certain biological processes showed that the coagulation of biocolloids was based on a protoplasm of various factors. In connection with the emergence of the teachings on polymers, the colloid chemistry of the protoplasm has gross into the biophysics of polymers, and, especially, polyelectrolytes.

Appearance chemical kinetics Also caused the emergence of a similar direction in biology. More Arrhenius is one of the founders of chemical kinetics, showed that the general laws of chemical kinetics are applicable to the study of kinetic patterns in living organisms and to individual biochemical reactions.

The successes of the use of physical and colloidal chemistry with an explanation of a number of biological phenomena were reflected in medicine.

The role of colloid and ion phenomena in the inflammatory process was revealed. Physico-chemical interpretation received the patterns of cell permeability and its changes in pathological processes, that is, physico-chemical (biophysical pathology).

With the development of biophysics in biology, accurate experimental research methods were penetrated - spectral, isotopic, radioscopic.

2. Models of the material point and absolutely solid. Motion parameters (radius vector, movement, speed, acceleration). The principle of inertia and its analysis.

Material point

In many kinematic tasks, it turns out to be possible to neglect the sizes of the body itself. Let us consider the car moving from Minsk to Brest. The distance between these cities is about 350 kilometers, the size of the car is a few meters, so in such a situation when describing the position of the car, you can not take into account its size - if the car's hood is in Brest from the right entrance of the desired home, then we can assume that its trunk is approximately Ibid. Thus, in this task, you can mentally replace the car with its model - body, the dimensions of which are negligible. Such a model of the body is very often used in physics and is called material point.

Material point - This is the ideal body model, the sizes of which in these conditions can be neglected.

The general geometric and material points is the absence of its own sizes. The material point, as necessary, can "endow" the properties that real bodies have, for example, weighing, energy, electric charge, and so on.

One of the criteria for the applicability of the model of the material point is the smallness of the sizes of the body compared to the distance to which it moves. However, this condition is not completely unequivocal. So, describing the movement of the Earth around the Sun when calculating its position in orbit, the dimensions of the Earth can be neglected, to consider it with a material point. However, if we need to calculate the times of sunrise and sunset, the material point model is fundamentally not applicable, as this description requires accounting for the rotation of the Earth, accounting for its size and form.

Consider another example. Sprinters compete on the Stater Distation. The purpose of the description of the movement is to identify who from the athletes runs through the distance in less time (the task is purely kinematic). Is it possible to count the runner in this task? His size is significantly less than the distance of the race, but are they small enough so that they could be neglected? The answer to these questions depends on the desired description accuracy. So, in serious competitions, time is measured with an accuracy of 0.01 seconds, during which time the runner shifts up to a distance of about 10 centimeters (a simple assessment obtained on the basis of mid speed Sprinter 10 m / s). Consequently, the error with which is determined by the position of the runner (10 cm) less than its transverse dimensions, therefore the material point model in this case is not applicable. It is not by chance that the wizard of the spinning run on the finish "throws the chest ahead", winning the precious hundredths of a second. Thus, the second criterion of the applicability of the model is the desired accuracy of the description of the physical phenomenon.

In some situations, you can use the material of the material point, even if the sizes of the body are comparable and even more distances to which the body is shifted. This is permissible when the position of one body point uniquely determines the position of the entire body. So when sliding the bar on the inclined plane, knowing the position of its center (as, however, and any other point) can be found the position of the entire body. If the model of the material point turns out to be inapplicable, then you need to use other more complex models.

Absolutely solid

With a progressive movement, all points of the body are obtained in the same period of time equal to the magnitude and direction of movement, as a result of which the speed and acceleration of all points at each time turn out to be the same. Accordingly, with progressive movement, all points of the body describe the same trajectories. Therefore, it is enough to determine the movement of one of the points of the body (for example, its center of inertia) in order to characterize the entire movement of the entire body.

In the rotational movement, all the points of the solid are moving around the circles, the centers of which lie on the same direct, called axis of rotation. The trajectories and linear velocities of different points are different, but the angles of rotation and angular velocities are the same. Since the angular velocities of all points of the body are the same, they are talking about the angular velocity of the body. To describe the rotational motion, you need to set a position in the space of the rotation axis and the angular velocity of the body at each moment of time.

When describing the rotational motion, it is believed that the body under consideration is not deformed, i.e., the distances between the points of the body do not change. Such a body in mechanics is called an absolutely solid body.

1.Toretical mechanics

2. Restracted materials

3. Details of cars

System forces. Equivalent systems forces. Equality. The main tasks of statics.

The line along which the force is carried out is called the strength line. Several forces acting on the body form the system of forces. In the statics we will talk about several systems of forces and identify equivalents of systems. Equivalent systems have an identical action on the body. All the forces acting in the statics will be divided into external and internal.

Asioms Static

Axiom 1. Inertia principle - any insulated material point is in a state of rest or uniform and rectilinear movement while the external forces applied to it will not derive it from this state. The state of rest or uniform rectilinear movement is called equilibrium. If the point or ATT is under the action of the strength system and retain equilibrium, the current system of forces is balanced.

Axiom 2. The conditions of equilibrium of the two forces. The two forces applied to ATT form a balanced system if they act, along one direct and in opposite sides and are equal to the module.

Axiom 3. The principle of attachment and exclusion of balanced forces. If the ATT acts the system of forces, then it can be added to it or from it you can take a balanced system of forces. The resulting new system will be equivalent to the initial one.

Corollary 1. The force applied to the solid body can be transferred to any point on the line of action, while the balance is not violated.

Axiom 4. Rules of the parallelogram and triangle. The two forces attached to the point have the equal diagonal applied in the same point the parallelogram is built on these forces as on the sides. Such an operation to replace the system of the forces of the resultant force is called the addition of forces. In some cases, the rules are used on the turn, i.e. The transformation of the unit forces of the convergent forces is carried out. The relative two forces applied to the point of the body is equal to the closing side of the triangle, the other side of which are equal to the initial forces.

Corollary 2. Theorem on the equilibrium of the three forces. If the three acting parallel forces are formed by the balanced system, the lines of the current forces intersect at one point.

Axioma 5. The law of action and counteraction. Upon contact of the two bodies, the force of the 1st body on the 2nd is equal to the strength of the 2nd body on the 1st with what both force act along the straight and are directed to the opposite sides.

System of convergent forces. Addition of a flat system of converging forces. Polygon.

The system of converging forces is such a system of forces acting on an absolutely solid body in which the line of action of all forces intersect at one point. The flat system of converging forces is such a totality of the body acting on the body, the line of action of which intersects at one point. Two forces acting on the body attached to one point form the simplest system of converging forces. For the operation of the addition of the system from a larger number of converging forces, the rule of building a power polygon is used. At the same time, the additions of the addition of two forces are consistent. The closing side of the polygon and will show the value of the direction of the vector of the resultant force.

Analytical equilibrium condition of a flat system of converging forces.

In place of construction of a power polygon, the resultant system of converging forces more accurately and faster is calculated using an analytical method. It is based on a projection method with which coordinate each system is projected on the coordinate axes and calculate the value of the projection. If you know the direction of the line of action relative to the axis x, the projection of this force on the coordinate axis is oh is taken with the function of the cosine and the projection of the force on the axis is taken with the function of force. If the condition of the problem direction of force is postponed from the OSA axis, the calculated scheme must be converted to calculating the angle between the force and the axis oh.

When determining the projection of forces on the axis OH and OU, there is a rule of signs on which we will determine the direction and according to the projection sign. If the force on the projection of the axis oh, the force coincides in the direction of the positive component, the projection of the force is taken with the sign "+. If the direction of force coincides with the area of \u200b\u200bthe negative values \u200b\u200bof the axis of the projection sign -. The same rule is characteristic of the AU axis.

If the force is parallel to one of the axes, the projection of force on this axis is equal to the power itself;

Projection of the same force on another axis. In the course of solving problems to determine the value of the resultant force analytically, this rule is used comprehensively, for example, for a given system of converging forces, a power polygon is constructed by the closing side of which is an equal system. We will spread this polygon on the axis of the coordinates and we define the magnitude of the projections of each existing force. Thus, the projection of the relay system of the convergent forces on each of the axes of coordinates is equal to the algebraic amount of the projections of the components on the tight axis. The numerical value of the resultant force is determined by the expression Fe \u003d FEX2 + Fey2 root. Tasks to determine the unknown forces of relations, characteristic of statics are solved by considering conditions. At the same time, the task is most often solved analytically and checking the correctness of the decision graphically. As a result, the power polygon should be closed.

Geometric equilibrium condition of a flat system of converging forces.

Consider the system of forces acting over the body and we define the value of the resultant. As a result of consistent addition, a vector of total force, which shows the action of the system forces on the body, however, the construction can simplify the passing intermediate stages to complete the vector of the resultant force at each stage. Building a power polygon can be conducted in any sequence. In this case, the value and direction of the vector of the automatic force are not changed. In statics, the system of forces of the forces acting on the body is considered balanced and if a certain direction to the magnitude of the resulting force is reduced after the operation of the formation of the forces - the closing side of the polygon, then in this system it is necessary to add strength numerically equal to the magnitude of the total vector of lying on one straight and oppositely directional. During the construction of a polygon, we see that the system of strength has an equally in order to comply with the statics conditions, the F5 is added, which balances the vector of the equal forces. As a result, F1 F2 F3 F4 F5 is balanced. Thus, the system of converging forces located in the plane is balanced when the power polygon is closed.

Complex traffic point.

Newton's laws are formulated to move the point in relation to inertial reference systems. To determine the kinematic parameters of the point when moving a relatively arbitrarily moving reference system, the theory of complex movement is introduced.

Complicated is the movement of the point in relation to two or several reference systems.

Figure 3.1.

Figure 3.1 shows:

Conditionally accepted for the fixed reference system O1x1y1Z1;

Moving relatively fixed Oxyz reference system;

Point M moving relative to the moving reference system.

Axioms speakers.

The principle of inertia, any insulated material system is in a state of rest or uniform and rectilinear movement while the applied external forces will not bring it from this state. This condition is called inertia. Inertia measures is body weight.

Mass - the amount of substance in the unit of body volume.

Newton's second law is the main law of dynamics. F \u003d Ma, where F is the active force, M- body weight, and - acceleration of the point.

Acceleration reported material point or system of points of force of a proportional value of force and coincides with the direction of force. For any point within the land, the force of gravity G \u003d Mg is valid, where G is the strength of gravity defining body weight.

The third law of Newton. The interaction forces of the two bodies are equal in size along one straight line in opposite sides. Dynamics in the interaction of two bodies acceleration is inversely proportional to the mass.

The law of independence of force. Each power of the system has the same effect on the material object as if it had acted alone at this acceleration that converts the body from the strength system equals the geometric amount of accelerations of the reported point by each force separately.

Work of gravity.

Consider moving the body along the trajectory with a substitutional height.

The work of gravity depends on changes in the height and is determined by W (B) \u003d G (H1-H2).

When lifting the body, the work of gravity is negative. Under the action of strength, resistance is carried out. When lowering the body, the work of gravity is positive.

Objectives and objectives of the "Machine Details" section. Mechanism and machine. Details and nodes. Requirements for machines, nodes and their details.

Machine-science parts studying the method of calculating and constructing machine parts and nodes.

In the development of contemporary Mechanical engineering highlight 2 trends:

1. Earth growth of the msinostroy increase the number and range of parts and general purpose nodes

2. The performance of the power and produces. Machine of their technologicality and, efficiency, weight and size of equipment.

The machine device is performed. Mechan. Movement for converting the energy of materials of motion materials in order to increase productivity and replace labor.

Divided into 2 groups:

Machines engines (DVS, Roating machine, electric motor)

Working machines (equipment, conveyors) and other devices facilitating or replacing physical work or logic. Human activity.

The mechanism is a set of interconnected links intended for converting the movement of one or more elements of the machine.

The elementary part of the mechanism consisting of several rigidly connected. Details - links. Input and output links, as well as leading and slave.

All machines and mechanisms consist of parts and nodes.

Detail of the product made of one material without assembly operations.

Node-finished. Assembly. Unit consisting of a number of details having a general functional purpose.

All items and nodes are divided into:

1. General purpose elements

A) Sodinit. Details and connections

B) Transfer of rotation. Moment

C) Details and nodes servicing. Shows

D) reference parts of cars

2. Special purpose elements.

Basic concepts about reliability and their details. Criteria for the performance and calculation of machine parts. Project and verification calculation.

Reliability is due to observance. Operation criteria is the property of a separate part or the entire machine to perform the specified functions while maintaining operational performance during a certain time interval.

Reliability depends on the features of the creation and operation of the machine. In the result of the operation of the machine with violations, faults cause loss.

The main indicator of reliability is the probability of trouble-free operation PT-coefficient of reliability, which shows the likelihood that in the time interval specified for the machine (in hours) fails. The result is determined. The probability of trouble-free operation according to the formula Pt \u003d 1-NT / N, where Nt is the number of machines or parts of the machine-failed service life, N - the number of machines and parts participating in expectation. The reliability of the entire car is generally equal to the PT \u003d PT1 * coefficient PT2 ... PTN. The following is one of the main quality indicators a machine that is associated with performance.

Operationability - the state of the object in which is able to perform the specified functions while maintaining the values \u200b\u200bof the specified parameters within the established technical and regulatory documentation.

The main criteria for the performance of D.M. is an:

Strength, rigidity, wear resistance, heat resistance, vibration resistance.

When designing D.M. Calculation is usually carried out according to one or two criteria, the remaining criteria are satisfied knowingly or do not have practical value The details under consideration.

Threaded connections. Classification of threads and basic geometric threads. Basic types of threads, their comparative characteristics and scope. Constructive forms of Tubes of the locking of threaded compounds.

The threaded is called the compound parts of the product with the use of the carving item.
The carving is obtained by cutting on the surface of the rod of the grooves when moving a flat figure - a thread profile (triangle, trapezoids, etc.)

Advantages of threaded connections
1) versatility,
2) High reliability,
3) Small dimensions and weight of fastening threaded parts,
4) the ability to create and perceive large axial forces,
5) The manufacturability and possibility of accurate manufacturer.

Disadvantages of threaded connections
1) a significant concentration of stresses in the places of a sharp change in cross section;
2) Low efficiency of movable threaded connections.

Classification of threads
1) in the form of the surface on which the carving is formed (Fig. 4.3.1):
- cylindrical;
- conical.

2) on the form of a thread profile:
- triangular (Fig. 4.3.2.a),
- Trapestials (Fig. 4.3.2.b),
- stubborn (Fig. 4.3.2.V),
- rectangular (Fig. 4.3.2.g) and
- Round (Fig. 4.3.2.).

3) in the direction of the helical line:
Right and left.
4) by number of goals:
Overcome, multipurpose (yields are determined from the end by the number of running turns).
5) For purpose:
-plus
-Wine-sealing,
-rest for moving transmission

The principle of operation and the device of friction gears with an unregulated (permanent) gear ratio. Advantages and disadvantages, scope. Cylindrical transmission. Materials rinks. Types of destruction of working surfaces of rollers.

Friction transmissions consist of two rinks (Fig. 9.1): the leading 1 and slave 2, which are pressed one to another force (in the figure - spring), so the friction force at the point of contact of the rolves is sufficient for the transmitted circumferential force.

Application.

Friction transmissions with an unregulated gear ratio in mechanical engineering are applied relatively rarely, for example, in friction presses, hammers, winches, drilling techniques, etc.). As the power gear, they are cumbersome and low-storey. These transmissions are used mainly in the devices where smoothness and silent operation are required (tape recorders, players, speedometers, etc.). They are inferior to gear transmissions in the bearing ability.

Fig.9.1. Cylindrical friction gear:

1 - leading rink; 2 - slave rink

A) Cylindrical friction gear is used to transmit motion between shafts with parallel axes.

B) The conical friction transmission is applied to the mechanisms at the axis of the shafts of which intersect.

Materials of rinks must possess:

1. Higher friction coefficient;

2. High power resistance parameter, strength, thermal conductivity.

3. High modulus of elasticity, the magnitude of which determines the load capacity.

Combines: steel steel, cast iron cast iron, steel composite materials.

The advantages of friction gear:

Smoothness and silent work;

Simplicity of structures and operation;

The possibility of stepless regulation of the gear ratio;

Protect mechanisms from breakdowns during overloads due to sliding the driving rink over the slave.

Disadvantages of friction gear:

Large loads on shafts and bearings due to the high force of pressed rollers;

The inconstancy of the gear ratio due to the elastic elastic slip rinks;

Increased wear of rinks.

The frictional transmission with parallel axes of the shafts and with the working surfaces of the cylindrical form are called cylindrical. One shaft diameter d X.install on fixed bearings, Bearings of another shaft with diameter d 2 -floating. Rollers 1 I. 2 fix on the shafts with a key and press one to another special device with force F r.Cylindrical friction transmissions with smooth rollers are used to transfer low power (in mechanical engineering to 10 kW); These programs are widely used in instrument making. For single-stage power cylindrical friction gears, it is recommended.

General About chain gears: principle of operation, device, advantages and disadvantages, scope. Chain gear details (drive chains, asterisks). Basic geometric ratios in transmission. Ratio.

Chain gears are applied in machines where the movement between the shafts is transmitted to. The distance (up to 8m) is used in the machines when the gear is not suitable, and the belt is not reliable. The machine is used in the machines from maximum power, with a circular speed of rotation up to 15 m / s.

Advantages (compared to belt):

More compact

Significant large capacity

Minor forces acting into engagement, which does not cause loading shafts.

Disadvantages:

1. Meeting noise when working

2. Welcome great wear in the chain

3. The presence in the design of the tensioner

4. Ready high price

5. Suggestion of manufacturing chain

The main element of the drive is a chain-consisting of a combination of hinges. Connected by the links. Construction of the chains standard and can be roller or gear. The pieces can consist of one or scolish rows. Along be durable, wear-resistant. Schedule gear wheels. Equity only in the profile of the tooth, where the chain falls during the operation of the transmission. The expansion is most effective with the maximum numerics of the teeth, a smaller sprocket.

The gear ratio is defined as u \u003d n1 / n2 \u003d z2 / z1. This value is focused from 1 to 6. If it is required to increase this value, then they make a chain transmission into several chains. CPD \u003d 96 ... 98%, and power loss occurs when the chain is friction About the asterisk and in supports.

Worm transmission with archimedean worm. Cutting worms and worm wheels. Basic geometric ratios. Slip speed in worm gear. Ratio. Forces acting in engagement. Types of destruction of worm wheels. Materials of worm pair units. Heat calculation of worm transmission.

Archimedes Worm has a trapezandal thread profile in the axial section. In the end section of the coil, the thread is contacted by the Archimedean Spiral. Archimedean worms are found in mechanical engineering, as the technology of their production is simple and most worked out. Archimedes worms are usually not grinding. They are used when the required worm material hardness does not exceed 350 HV. If you need to grind the working surfaces of turns of threads, conveyed and eructural worms prefer, which grinding which is easier and cheaper compared to the archimedean worm.

Archimedean Worms are similar to the tracking screws with trapezoidal carvings.The main methods of their manufacture are: 1. Cutting with a cutter on a turning and screw machine (see Figure 5.4). This method is accurate, but low-performance. 2. Cutting the modular cutter on a threadless machine. The method is more productive.

Fig. 5.7. Winter wheel cutting diagram:
1 - milling cutter; 2 - Billet wheels
The working capacity of the worm gear depends on the hardness and roughness of the coil surface of the worm thread, so after cutting the thread and heat treatment, the worms are often grinding, and in some cases polished. Archimedean worms are used without grinding threads, since for grinding them requires circles of a shaped profile that
It makes it difficult to process and reduces the accuracy of manufacture. Evolvent worms can be grinding the flat side of the circle on special worm-grinding machines,
Therefore, the future is behind the evolvent worms.
The worm wheels are most often cut by worm mills [Fig. 5.7), and the worm mill must represent a copy of the worm,with which the worm wheel will be engaged. When cutting the workpiece of the wheel and the milling cutter make the same mutual movement that the worm and worm wheel will have when working.

Basic geometric parameters

Alpha \u003d 20 0 -Profile angle

p-step teeth worm and wheels, appropriate dividing circumference worm and wheels

m-axial module

z 1-covered worms

d 1 \u003d Q * M-diameter of the dividing circle

d a 1 \u003d D 1 + 2M-diapaosone area. Speaker

d \u003d D 1 -2.4m-diameters of the circumference of the depression

wormworm coat worm running time skill with worm wheel teeth.
Slip speed v SC. (Fig. 5. 11) is aimed at the tangent of the worm divisory cylinder. As a relative speed, the sliding speed is easily determined through the circumferential velocity of the worm and wheels. District Cherry Speed \u200b\u200b(m / s)
District wheel speed (m / s)

Fig.5.11

^ Power in engagement
In the worm handle, as in the gears, the power of the worm is perceived not one, but a few teeth of the wheels.
To simplify the calculation of the power of the worm and wheels F N.(Fig. 5.12, but)take focused and attached in the pole
Turnworm
Fig. 5.12. Scheme of forces operating in worm engagement
engagement Pon the normal to the working surface of the turn. According to the rulelelepiped rule F N.lay out in three mutually perpendicular directions to the components F a, f n, f a1.For clarity, the image of the forces in fig. 5.12, B worm engagement is spread.
District force on the worm F T1 is numerically equal to the axial strengthon a worm wheel F a2.
F n \u003d f a2 \u003d 2t 1 / d 1,(5.25)
Where T 1.- Rotating moment on the worm.
District force on a worm wheel F T2 is numerically equal to the axial strength on the worm F A1:
F t2 \u003d f a1 \u003d 2t 2 / d 2,(5.27)
Where T 2. - Rotating moment on a worm wheel.
Radial force on the worm F R1 is numerically equal to radial power on the wheel F R2(Fig. 5.12, in):
F R1 \u003d F R2 \u003d F T2 TGA.(5.28)
The directions of the axial forces of the worm and a worm wheel depend on the direction of rotation of the worm, as well as on the direction of the turn line. Direction of power F T2.always coincides with the direction of the wheel rotation, and the power F N.directed to the side, the opposite speed of the worm rotation.

Worm gear works with large heat dissipation. In a significant allocation of oil, there is a danger of transferring the transmission, therefore the heat balance equation is compiled so that the amount of heat released at the maximum transmission load.

Slip bearings.

PS are supports of axes and shafts, perceive. Load and evenly distributing it on the housing of the node. From the bearings of a significant extent depends on the reliability of machines. In the sliding bearings, the 2nd surfaces are isolated-along the outer bearing, it is rigidly installed in the housing, and on the inner contact with the rotation. Shaft or axis as a result between submits. And the whipping is friction, which leads in cases of continuous exploitation of the bearing to heating and wear. For reducing the surface of the shaft and bearing applied lubrication.

Dignity PS:

Maintains performance at very high angular spin speeds

The bearing structures are shattering and blows, vibrations, due to the action of the oil layer.

Ensuring. High accuracy shaft installation

Ability to create a detachable design

Min. Radial dimensions

Silent work

Disadvantages of PS:

Large losses for overcoming friction force, especially when starting the car

The need for permanent bearing care Alver high lubrication requirements.

PS applies:

1. High-speed machines.

2.Valy complex form

3. Work in machines with aggressive environments and water

4. For the mechanisms of the slave. With shocks and blows

5. For nearly arranged axes and shafts with small radial gaps

6.Inxious few responsible mechanisms and machines.

By design, the housing of the bearing can be:

1. It is possible. It is not possible to compensate for the wear of the bearing. It is applied to the axes of axes and shafts working with a small load.

2. Dravel housing consists of two separate elements of compounds that are causing. By installing the bearing into the working machine.

Rolling bearings.

Rolling bearings are a ready-made node, the main element of which are rolling bodies - balls 3 or rollers installed between rings 1 and 2 and held at a certain distance from each other by a rope called separator 4.

In the process of working the body, rolling rolling tracks, one of which is in most cases non-moving. The distribution of the load between the carriers of rolling bodies is uneven and depends on the magnitude of the radial clearance in the bearing and on accuracy geometric shape His details.

In some cases, to reduce the radial sizes of the ring bearing there are no and rolling bodies roll directly along the pin or body.

Rolling bearings are widespread in all sectors of mechanical engineering. They are standardized and amid in bulk production on a number of large specialized factories.

Advantages and disadvantages of rolling bearings

Advantages of rolling bearings:
Comparatively low cost due to the mass production of bearings.
Small friction losses and insignificant heating (friction losses when starting and steady mode of ra-bots are almost the same).
High degree Interchangeability, which facilitates the installation and repair of machines.
Small consumption of lubricant material.
Do not require special attention and care.
Small axial sizes.
Disadvantages of rolling bearings:
High sensitivity to shock and vibration loads due to the large stiffness of the structure of the bearing.
Mullese in high-speed drives due to excessive heating and danger of separator destruction from centrifugal forces.
Reparatively large radial sizes.
Noise at high speeds.

In the form of the bodies of rolling, rolling bearings are classified on:
balls (a);
roller.
Roller rolling bearings can be with:
cylindrical rollers (b);
conical rollers (B);
barrel rollers (g);
needle rollers (D);
twisted rollers (e).

In the direction of the perceived load, rolling bearings are classified on:
radial;
radially resistant;
stubborn radial;
Stubborn.
According to the number of rows of rolling, rolling bearings are divided into:
single row;
multi-row.
By the ability to self-establish rolling bearings divide on:
self-aligning;
Uncommmable.
In the dimensions, rolling bearings are divided into the series.

Rolling bearings series and their designation

For each type of bearing with one and the same internal diameter there are various series, distinguishing with sizes of rings and rolling bodies.
Depending on the size of the outer diameter, the bearings are:
ultralight;
Especially light (1);
Light (2);
Average (3);
Heavy (4).
Depending on the width of the Bearing series, divided into:
especially narrow;
narrow;
normal;
wide;
Especially wide.
Rolling bearings are marked by applying a row of numbers and letters to the end, conventionally denoting insections of diameter, series, type, design varieties, accuracy class, etc.
The two first digits on the right indicate its inner diameter D. For bearings with d \u003d 20..495 mm, the size of the internal diameter is determined by multiplying the specified two digits by 5. The third digit on the right indicates a series of diameters from a particularly light series (1) to severe (4). The fourth digit on the right indicates the type of bearing:

Technical mechanics as science consists of 3 sections:

1.Toretical mechanics

2. Restracted materials

3. Details of cars

In turn, the theoretical mechanics consists of 3 subsections:

1. Latics (studying forces acting on the bodies)

2. Cinematics (studies the equation of body traffic)

3. Dynamics (studies the movement of bodies under the action of forces)

Material point. Absolutely solid body. Force; Units of power.

The material point is a geometric point with a mass.

Absolutely solid body is a material object, the distance between two points on the surface of which always remains constant. This is also an absolutely rigid. Any ATT can be viewed as a system of material points. Measure mechanical effects of one material object on the 2nd is the power. (H)

Power - a vector value that is characterized by a direction, an application point, a numerical value or a module of force.

Mechanics

Physics subject- Science studying the general and simplest properties and laws of motion of the substance and fields.

Physical model- It is called his mathematical model made up of ideal physical objects.

Physical model- Abstract concepts used to describe traffic motion depending on specific tasks.

The basis of classical mechanics lie next. Representations of space and time. The physical space is considered as a three-dimensional Euclide space, and the time is considered independent of the material bodies and everywhere is the same.

Classical mechanics- There is a movement of macroscopic bodies with speeds, small compared to the speed of light, the laws are based on Newton.

Kinematics- Science, studying the state of movement, regardless of the forces causing.

Kinematics (Greek. κινειν - move) in physics - section of mechanics learning a mathematical description (means of geometry, algebra, mathematical analysis ...) movements of idealized bodies (material point, absolutely solid, perfect liquid), without consideration of the causes of movement (mass, forces and forces and etc.). The initial concepts of kinematics are space and time. For example, if the body moves around the circumference, the kinematics predicts the need for the existence of a centripetal acceleration without clarifying what nature is power, its generating. The reasons for the occurrence of the mechanical movement is engaged in another section of mechanics - dynamics.

The main task of mechanics - determine the position of the body at any time.

Mechanical movement - This is a change in body position in space over time relative to other bodies.

Reference system- Assumption of fixed relative to each other bodies in relation to which the movement is considered and counting the time of hours.

Methods of task material point- It is easy to specify the positions and speed of all bodies forming the system.

Absolutely solid body - the second reference object of mechanics along with the material point.

Many real bodies are solid, that is, for a long time, retain their sizes and shape, more precisely, the changes in size and the form are so insignificant that they can be neglected. The model of such bodies is absolutely

solid.

Absolutely solid body - This is the perfect model of the body, a change in the size and forms of which in these conditions can be neglected.

From this definition it follows that the distances between the two any points of the absolutely solid remains unchanged. Absolutely solid can also be considered as a set of material points, rigidly interconnected. So

the position of the ocean liner in the open sea can be described, using the model of the material point, and its spatial orientation (course, tilt) with the help of an absolutely solid model. The applicability of the model of an absolutely solid body is due only to a specific problem under study - the purpose of modeling and the required accuracy.

Thus, the position of the absolutely solid body is fully determined, for example, by the position of the coordinate chosen coordinate system rigid to it (usually its origin coordinates make coinciding with the center of solid masses).

IN three-dimensional space And in the absence of (other) connections, the absolutely solid body has 6 degrees of freedom: three progressive and three rotational. The exception is a ductomic molecule or, in the language of classical mechanics, a solid rod of zero thickness. Such a system has only two rotational degrees of freedom.

Reference system - This is a combination of the reference body associated with it the coordinate system and the time reference system, relative to which the movement (or equilibrium) is considered by any material points or tel.

Mathematically, the movement of the body (or material point) relative to the selected reference system is described by the equations that establish how they change over time t. Coordinates defining the position of the body (point) in this reference system. These equations are called movement equations. For example, in the Cartesian coordinates x, y, z, the movement of the point is determined by the equations ,,

IN modern physics Any movement is relative and the movement of the body should be considered only in relation to any other body (sample body) or body system. You can not specify, for example, how the moon moves in general, it is only possible to determine its movement, for example, in relation to Earth, the Sun, stars, etc.

Material dot (particle)- This is the body, the sizes of which in the conditions of this task can be neglected.

Absolutely solid body

Absolutely solid body - the second reference object of mechanics along with the material point. The mechanics of an absolutely solid body are fully reduced to the mechanics of material points (with superimposed connections), but has its own content (useful concepts and relations that can be formulated within the framework of an absolutely solid body) representing a large theoretical and practical interest.

There are several definitions:

Absolutely solid body - the model concept of classical mechanics, denoting the totality of material points, the distance between which is preserved in the process of any movements made by this body. In other words, an absolutely solid body not only does not change its form, but also retains the mass distribution inside.
Absolutely solid body is a mechanical system, which has only progressive and rotational degrees of freedom. "Hardness" means that the body cannot be deformed, that is, the body cannot be transferred to any other energy, except for the kinetic energy of the progressive or rotational motion.
Absolutely solid body - body (system), the mutual position of any points of which does not change, in whatever processes it does not participate.

Thus, the position of the absolutely solid body is fully determined, for example, by the position of the coordinate chosen coordinate system rigid to it (usually its origin coordinates make coinciding with the center of solid masses).

In three-dimensional space and in the absence of (other) connections, there is absolutely solid body with 6 degrees of freedom: three progressive and three rotational. The exception is a ductomic molecule or, in the language of classical mechanics, a solid rod of zero thickness. Such a system has only two rotational degrees of freedom.

Absolutely solid bodies in nature do not exist, however, in very many cases, when the deformation of the body is small and it can be neglected, the real body may (approximately) are considered as an absolutely solid body without prejudice to the task.

As part of relativistic mechanics, the concept of an absolutely solid body is internally contradictory, which shows, in particular, the paradox of Ehrenthest. In other words, the model of an absolutely solid body generally speaking is completely non-applicable to the case of fast movements (comparable at speed at the speed of light), as well as to the case of very strong gravitational fields.

Dynamics of absolutely solid body

The dynamics of the absolutely solid body is fully determined by its complete mass, the position of the center of mass and the inertia tensor (as well as the dynamics of the material point - its mass). (Of course, it is understood that all external forces and external communications are given, which, of course, may depend on the shape of the body or its parts, etc.).

In other words, the dynamics of an absolutely solid body with unchanged external forces depends on the distribution of its masses only through the full mass, the center of mass and the inertia tensor, the rest of the mass distribution of the absolutely solid body will not affect its movement; if somehow so redistributing the masses inside the absolutely solid body, which will not change the center of masses and the inertia tensor, the movement of the solid in the specified external forces will not change (although at the same time maybe change and usually change internal stresses In the solid body!).

Private definitions

Absolutely solid body on the plane is called flat rotator. It has 3 degrees of freedom: two progressive and one rotational.

Absolutely solid body with one fixed point, unable to rotate and placed in the gravity field, called physical pendulum.

Absolutely solid body with one fixed point, but able to rotate, called wolf.

Notes

Literature

Suslov G. K. "Theoretical Mechanics". M., "Gostekhizdat" 1946
Appel P. "Theoretical Mechanics" TT. 1.2. M. "Fizmatgiz" 1960
Cetaev N. G. "Theoretical Mechanics". M. "Science" 1987
Markeev A. P. "Theoretical Mechanics". M. "Science" 1999
Golubev Yu. F. "Fundamentals of theoretical mechanics." M., Publishing House Mosk. UN-TA, 2000
Zhuravlev V. F. "The foundations of theoretical mechanics." M., "Science" 2001

Link

Wikimedia Foundation. 2010.

Watch what is "absolutely solid body" in other dictionaries:

absolutely solid body

absolutely solid body - Absoliučiai Standus Kūnas Statusas T Sritis Fizika Atitikmenys: Angl. Perfectly Rigid Body Vok. ABSOLUT STARRER KÖRPER, M RUS. Absolutely solid body, N PRANC. Corps Parfaitement Rigide, M; SOLIDE PARFAIT, M ... Fizikos Terminų žodynas

The solid body model, which is considered undersized in any impacts (Bulgarian language; Bellgarski) absolutely tyrotina (Czech language; Čeština) Dokonale Tuhé Těleso ( German; Deutsch) Nicht verformbarer Körper; Absolut Starrer ... ... Construction Dictionary

solid - absolutely solid body; The solid body is a material body, in which the distance between two any dots always remains unchanged ... Polytechnic Terminology Dictionary

Model location of atoms in a solid body crystal solid body is one of four aggregate states Substances that differ from other aggregate states (liquid, gases ... Wikipedia

Absolutely solid body in mechanics Mechanical system, which has only progressive and rotational degrees of freedom. "Hardness" means that the body can not be deformed, that is, the body can not be transferred to any other energy, except ... ... Wikipedia

Absolute (lat. Absolutus finished, unlimited, unconditional, perfect) absolute means something that is being considered in itself, without attitudes to anything else, is opposed to relative. Values \u200b\u200bin philosophy: Absolute ... ... Wikipedia

The body, or physical body in physics material object having a mass and separated from other borders of the section. The body is the form of the existence of a substance. See also absolutely solid body absolutely black body deformable material material ... ... Wikipedia

- (from Greek. Statike Teaching about weight, about equilibrium), section of mechanics devoted to the study of the equilibrium of material bodies under the action of forces. C. shared on geometric and analytical. At the heart of analytic. S. lies possible movements principle ... Physical encyclopedia

- (from Greek. Statike Teaching about weight, about equilibrium) Section of mechanics dedicated to the study of the equilibrium of material bodies under the action of forces. C. shared on geometric and analytical. At the heart of the analytical S. lies with the possible ... ... Great Soviet Encyclopedia

The easiest way to describe the movement of the body, the mutual partition of parts of which does not change. Such a body is called absolutely solid.
When studying kinematics, we said that it means to describe the body movement - it means to describe the movement of all its points. In other words, it is necessary to be able to find the coordinates, speed, osko-rhenium, the trajectories of all points of the body. In general, this is a difficult task, and we will not try to solve it. It is especially difficult when the bodies are noticeably deformed during the movement.
The body can be considered absolutely solid if the distances between two any points of the body are unchanged. In other words,
the form and dimensions of the absolutely solid bodies do not change under the action of any forces on it.
In fact, there are no such bodies. This is a physical model. In cases where deformations are small, you can consider real bodies as absolutely solid. However, the solid movement in the general case is difficult. We will focus on the two, most simple types of solid movement: progressive and rotational.
Protective traffic
The solid is moving progressively, if any segment of a straight line, rigidly associated with the body, moves all the time in parallel to itself.
With progressive movement, all points of the body make the same movement, describe the same paths, pass the same paths, have equal speed and acceleration. Show it.
Let the body move progressively. Connect two arbitrary points A and in the body with a straight line (Fig. 7.1). Cut AB should remain parallel to itself. The distance AU does not change, as the body is absolutely solid.
In the process of translational movement, the vector AB is not from-changing, that is, its module and direction remain constant. As a result, the trajectory of points A and in identical ^ as they can be fully combined by parallel transfer on AV.
It is easy to notice that moving points A and in the same and committed in the same time. Consequently, points A and B have the same speeds. They are the same and acceleration.
It is clear that to describe the progressive movement of the body, it is enough to describe the movement of any one of its point, since all points move the same. Only in this movement can be told about body velocity and acceleration. With any other movement of the body of its point, there are different speeds and accelerations, and the terms "body velocity" or "body acceleration" lose meaning.

Approximately adjoining the box of the written table, the pistons of the car engine relative to cylinders, wagons on the straight line railway, Cutter of the lathe relative to the bed (Fig. 7.2), etc. The transparent can be considered and movements with a rather complicated appearance, such as the movement of the bike pedal or cabin of the Ferris Wheels (Fig. 7.3) in the parks.
Rotary traffic
Rotational motion around the stationary axis is another type of solid movement.

shshsh "Fig. 7.3.
The rotation of the solid around the stationary axis is called such a movement, in which all points of the body describe the circles whose centers are located on one straight line, perpendicular to the planes of these circles. This direct is the axis of rotation (Mn in Figure 7.4).

In the technique, such a type of movement occurs extremely often: rotation of the shafts of engines and generators, wheels of modern high-speed electric trains and rustic carts, turbines and propellers of aircraft, etc. The earth rotates around its axis.
For a long time it was believed that in living organisms of devices like a rotating wheel, no: "Nature has not created the wheels." But research recent years showed that it is not_. In many bacteria, for example, in the intestinal stick, there is a "motor", rotating flagella. With the help of these bundles, bacteria moves in the medium (Fig. 7.5, a). The base of the flavor is attached to the wheel (rotor) in the form of a ring (Fig. 7.5, b). The plane of the rotor is parallel to another ring fixed in the cell membrane. The rotor rotates, making up to eight revolutions per second. The mechanism leading the rotor in rotation remains so far not clear.
Kinematic description
rotational Movement of the Solid Body
When the body is rotated, the radius of the circle described in the point and this body (see Fig. 7.4), will turn over the time interval at some CP angle. It is easy to see that due to non-change mutual location Body points on the same angle f turn over the same time and radii of circles described by any other points of the body (see Fig. 7.4). Consequently, this angle F can be considered a value characterized by a movement of not only a separate point of the body, but also the rotational movement of the entire body as a whole. Therefore, it is enough to describe the rotation of the solid body around the stationary axis - the variable F (0.
This single value (coordinate) and can be the angle of F, which is rotated by the body around the axis relative to some of its position taken for zero. This position is defined by axis 0, x in Figure 7.4 (segments 02V, OAB parallel to OGH).
In § 1.28, the movement of the circumference point was considered. The concepts of the angular velocity of the CO and the angular acceleration of p were introduced. Since, when the solid is rotated, all of its points for the same time intervals rotate to the same angles, then all formulas describing the movement of the circumference point are applied and to describe the rotation of the solid. The determination of the angular velocity (1.28.2) and the angular acceleration (1.28.6) can be attributed to the rotation of the solid. Similarly, formulas (1.28.7) and (1.28.8) to describe the movement of the solid with a constant angular acceleration.
The connection between linear and angular velocities (see § 1.28) for each point of the solid is given by the formula
and \u003d (7.1.1)
where R is the distance of the point from the axis of rotation, i.e. the radius of the circle described by the point of the rotating body. Directional speed is directed on the tangent of this circle. Different points of solid body have different linear speeds at the same angular velocity.
Different points of solid body have normal and tangential accelerations, determined by formulas (1.28.10) and (1.28.11):
ap \u003d S2D, AT \u003d RD. (7.1.2)
Flat-parallel motion
Flat-parallel (or simply flat) movement of the solid is called such a movement in which each body point moves all the time in the same plane. And all the planes in which the points are moving are parallel to each other. A typical example of a plane-parallel movement is to combine the cylinder on the plane. Flat-parallel is also the movement of the wheel along the direct rail.

Recall (for once again!), As you can talk about the nature of the movement of a body, only with respect to a certain reference system. Thus, in the above examples in the reference system associated with rail (land), the movement of the cylinder or wheel is plane-parallel, and in the reference system associated with the wheel axis (or cylinder), rotational. Consequently, the velocity of each point of the wheel in the reference system associated with the Earth (absolute speed) according to the law of the addition of speeds is equal to the vector sum of the linear speed of the rotational motion (relative speed) and the speed of the progressive movement of the axis (portable speed) (Fig. 7.6 ):
Instant center of rotation
Let the thin disk roll on the plane (Fig. 7.7). Circle can be viewed as the right polygon with an arbitrarily large number of parties. Therefore, the circle shown in Figure 7.7 can be mentally replaced with a polygon (Fig. 7.8). But the movement of the latter consists of a number of small turns: first around the point C, then around the points Cj, C2, etc. Therefore, the disk movement can also be considered as a sequence of very small (infinitely small) turns around the points C, CX, C2, etc. d. Thus, at each time the disk rotates around its lower point C. This point is called the instantaneous disk rotation center. In the case of rolling the disk on the plane, you can talk about the instantaneous axis of rotation. This axis is the line of contact with the plane in this moment time. Fig. 7.7
Fig. 7.8.
The introduction of the concept of an instantaneous center (instant axis) of rotation simplifies the solution of a number of tasks. For example, knowing that the disk center has speed and, you can find the speed of point A (see Fig. 7.7). Indeed, since the disk rotates around the instant center C, then the radius of rotation of the point A is equal to the AU, and the radius of rotation of the point is equal to the OS. But since ac \u003d 2 ° C, then? "about
va \u003d 2v0 \u003d 2v. Similarly, you can find the speed of any point of this disk.
We got acquainted with the simplest types of solid movement: progressive, rotational, flat-parallel. In the future, we have to do the dynamics of a solid body.