Movement around the circumference. Definition of physics. Uniform Movement around the circle

Since the linear speed changes evenly direction, then the movement in the circumference can not be called to the meal, it is valuable.

Angular velocity

Select the point on the circle 1 . We construct a radius. Per unit time point will move to the item 2 . In this case, the radius describes the angle. The angular velocity is numerically equal to the angle of rotation of the radius per unit of time.

Period and frequency

Rotation period T.- This is the time for which the body makes one turn.

Rotation frequency is the number of revolutions in one second.

Frequency and period are interconnected by the ratio

Communication with angular speed

Line speed

Each point on the circle moves at some speed. This speed is called linear. The direction of the linear velocity vector always coincides with the tangent of the circumference.For example, sparks from under the grinding machine are moving, repeating the direction of instantaneous speed.

Consider the point on the circle that makes one turn, the time that spent is a period T..We, which overcomes the point is the length of the circle.

Centripetal acceleration

When driving around the circle, the acceleration vector is always perpendicular to the velocity vector, directed to the center of the circle.

Using previous formulas, you can derive the following ratios

Points lying on one straight line outgoing from the center of the circle (for example, it may be points that lie on the wheel knitting), will have the same angular velocity, period and frequency. That is, they will rotate equally, but with different linear speeds. The further point from the center, the faster it will move.

The law of addition of speeds is fair and for rotational motion. If the movement of the body or reference system is not uniform, the law is used for instantaneous speeds. For example, the speed of a person walking along the edge of the rotating carousel is equal to the vector sum of the linear speed of rotation of the edge of the carousel and the speed of the human movement.

The land participates in two main rotational movements: daily (around its axis) and orbital (around the sun). The period of rotation of the Earth around the Sun is 1 year or 365 days. Around its axis, the Earth rotates from the West to the East, the period of this rotation is 1 day or 24 hours. The latter is called the angle between the plane of the equator and the direction from the center of the Earth to the point of its surface.

According to Newton's second law, the cause of any acceleration is power. If the moving body is experiencing centripetal acceleration, the nature of the forces, the action of which caused by this acceleration may be different. For example, if the body moves around the circle on the rope tied to it, then acting power is the power of elasticity.

If the body lying on the disk rotates with the disk around its axis, then the force of friction is such force. If the power stops its action, then the body will move in a straight line

Consider moving the point on the circle from A in B. Linear speed is equal

We now turn into a fixed system associated with the Earth. The complete acceleration of the point A will remain the same and in the module, and in the direction, since when switching from one inertial reference system to another acceleration does not change. From the point of view of the fixed observer, the trajectory of points A is no longer a circle, but a more complex curve (cycloid), along which the point moves unevenly.

Among different species curvilinear movement is of particular interest uniform body movement around the circumference. This is the easiest type of curvilinear movement. At the same time, any complex curvilinear movement of the body on a sufficiently small plot of its trajectory can be approximately considered as a uniform movement around the circle.

Such a movement make points of rotating wheels, turbine rotors, artificial satellites, rotating in orbits, etc. uniform motion By circumference, the numerical value of the speed remains constant. However, the direction of speed with this movement is continuously changing.

The body speed at any point of the curvilinear trajectory is aimed at tangent to the trajectory at this point. This can be convinced of this, watching the work sharpened having a disc shape: clustering to a rotating stone The end of the steel rod can be seen from the stone hot particles. These particles fly at the speed they possessed at the time of the separation of stone. The departure direction of the spark always coincides with the tangent of the circumference at that point, where the rod touches the stone. On the tangent of the circle, the splashes from the wheels of the bucking car are also moving.

Thus, the instantaneous body rate at different points of the curvilinear trajectory has different directions, while the speed module can be the same or everywhere, or change from point to point. But even if the speed module does not change, it can not be considered constant anyway. After all, the speed is the magnitude of the vector, and for vector quantities, the module and direction are equally important. therefore curvilinear movement is always acceleratedEven if the speed module is constant.

With curved motion, the speed module and its direction may vary. A curvilinear movement at which the speed module remains constant, called uniform curvilinear movement. Acceleration with this movement is associated only with a change in the direction of the velocity vector.

Both the module and the direction of acceleration should depend on the form of a curve trajectory. However, there is no need to consider each of its countless forms. Representing each site as a separate circumference with some radius, the task of finding acceleration in curvilinear uniform movement will be reduced to finding acceleration with uniformized body movement around the circle.

Uniform movement around the circle is characterized by a period and frequency of circulation.

The time for which the body makes one turn is called a period of circulation.

With a uniform movement around the circle, the period of circulation is determined by the division of the traveled path, i.e. the length of the circle to the speed of movement:

The value, reverse period, is called frequency of circulation, denotes the letter ν . Number of revolutions per unit time ν Call frequency of circulation:

Due to the continuous change in the direction of speed, the body moving around the circle has acceleration, which characterizes the speed of changes to its direction, the numerical value of the speed in this case does not change.

With uniform body movement around the circle, the acceleration at any point is always directed perpendicular to the speed of the movement along the radius of the circle to its center and is called centripetal acceleration.

To find its value, consider the ratio of changes in the velocity vector to the time interval for which this change occurred. Since the angle is very small, then we have.

Alexandrova Zinaida Vasilyevna, Teacher of Physics and Informatics

Educational institution: MBOU SOSH No. 5 P. Pechenga, Murmansk region.

Thing: physics

Class : Grade 9.

Theme lesson : The movement of the body around the circumference with constant modulo speed

The purpose of the lesson:

give an idea of \u200b\u200bcurvilinear movement, introduce the concepts of frequency, period, angular velocity, centripetal acceleration and centripetal force.

Tasks lesson:

Educational:

Repeat the types of mechanical movement, introduce new concepts: Movement around the circle, centripetal acceleration, period, frequency;

To identify in practice the connection of the period, frequency and centripetal acceleration with the radius of circulation;

Use training laboratory equipment to solve practical tasks.

Developing :

Develop the ability to apply theoretical knowledge to solve specific tasks;

Develop a culture of logical thinking;

Develop interest in the subject; cognitive activity When setting and conducting an experiment.

Educational :

To form a worldview in the process of studying physics and argue its conclusions, to bring up independence, accuracy;

Educate the communicative and information culture of students

Equipment of the lesson:

computer, projector, screen, presentation to the lesson "Body Movement around Circle », printing cards with tasks;

tennis ball, badminton wave, Toy car, thread ball, tripod;

sets for the experiment: Stopwatch, tripod with clutch and paw, ball on the thread, line.

Form of training organization: Frontal, individual, group.

Type of lesson: Study and primary consolidation of knowledge.

Educational and Methodical Provision: Physics. Grade 9. Textbook. Pryrickin A.V., Godnik E.M. 14th ed., Ched. - M.: Drop, 2012

Time to implement lesson : 45 minutes

1. The editor in which the multimedia resource is made:MS.PowerPoint.

2. View of the Multimedia Resource: Visual Presentation educational material Using triggers, embedded video and interactive test.

Lesson plan

Organizing time. Motivation to educational activities.

Actualization of reference knowledge.

Studying a new material.

Conversation on issues;

Solving problems;

Implementation of research practical work.

Summing up the lesson.

During the classes

Stages lesson

Temporary implementation

Organizing time. Motivation to educational activities.

Slide 1. ( Check readiness for lesson, announcement of the theme and lesson purposes.)

Teacher. Today at the lesson you will learn what acceleration with uniform body movement around the circle and how to determine it.

2 minutes

Actualization of reference knowledge.

Slide 2.

F.iceed dictation:

Changing the position of the body in space over time.(Traffic)

The physical value is measured in meters.(Move)

Physical vector magnitude characterizing the speed of movement.(Speed)

The main unit of measurement of length in physics.(Meter)

The physical quantity, the units of measurement of which serve the year, day, hour.(Time)

The physical vector value that can be measured using an accelerometer device.(Acceleration)

Length of trajectory. (Way)

Acceleration units (m / s 2 ).

(Conducting a dictation with subsequent inspection, self-assessment of works by students)

5 minutes

Studying a new material.

Slide 3.

Teacher. We often observe such a movement of the body, in which its trajectory is a circle. The circle moves, for example, the wheel rim when it rotates, the points of rotating parts of the machines, the end of the clock arrow.

Demonstration of experiments 1. Falling a tennis ball, a flight of a volan for badminton, moving a toy car, ball oscillations on a thread attached to a tripature. What is common and how do these movements differ?(Pupil Answers)

Teacher. Straight traffic - This is a movement whose trajectory is a straight line, curvilinear - curve. Give examples of rectilinear and curvilinear movement with which you met in life.(Pupil Answers)

Body movement around the circle isa special case of curvilinear movement.

Any curve can be represented as an amount of arc circles of different (or identical) radius.

The curvilinear movement is called such a movement that is performed on arcs of circles.

We introduce some characteristics of the curvilinear movement.

Slide 4. (View video " speed.avi " According to the link on the slide)

Curvoline movement with a constant speed module. Movement with acceleration, because Speed \u200b\u200bchanges direction.

Slide 5. . (View video "The dependence of the centripetal acceleration from radius and speed. Avi. »By reference to the slide)

Slide 6. The direction of velocity and acceleration vectors.

(Working with the materials of the slide and analysis of the drawings, the rational use of the effects of animation embedded in the elements of the drawings, Figure 1.)

Fig.1.

Slide 7.

With a uniform body movement around the circle, the acceleration vector is perpendicular to the velocity vector, which is directed along the tangent of the circle.

The body is moving around the circumference provided that vector linear speed is perpendicular to the centripetal acceleration vector.

Slide 8. (Working with Slide Illustrations and Materials)

Centripetal acceleration - Acceleration with which the body moves around the circumference with constant modulo speed, is always directed along the circle radius to the center.

a. c. =

Slide 9.

When driving around the circle, the body will return to the initial point at a certain period of time. Movement around the circle - periodic.

Treatment period - this time intervalT. during which the body (point) makes one turn around the circumference.

Unit of measurement of the period -second

Rotation frequency  - The number of full revolutions per unit of time.

[  ] \u003d S. -1 \u003d Hz

Frequency measurement unit

Post Post 1. The period is a magnitude that is often found in nature, science and technology. Earth revolves around his axis, midnight This rotation is 24 hours; The total turnover of the Earth around the Sun is approximately 365.26 days; Helicopter screw has an average period of rotation from 0.15 to 0.3 s; The blood circulation period in humans is approximately 21 - 22 s.

Post post 2. The frequency is measured by special devices - tachometers.

Technical Device Rotation Frequency: A gas turbine rotor rotates with a frequency of 200 to 300 1 / s; A bullet, flying out of the Kalashnikov machine, rotates with a frequency of 3000 1 / s.

Slide 10. Communication of a frequency period:

If, during T, the body made n full revolutions, then the treatment period is:

The period and frequency are the convergent values: the frequency is inversely proportional to the period, and the period is inversely proportional to the frequency

Slide 11. The speed of body treatment is characterized by angular speed.

Angular velocity(cyclic frequency) - the number of revolutions per unit of time expressed in radians.

Corner speed - angle of rotation to which the point turns during the timet..

The angular speed is measured in rad / s.

Slide 12. (View video "Path and movement with curvilinear movement.avi" according to the link on the slide)

Slide 13. . Motion kinematics in the circumference.

Teacher. With a uniform movement around the circle, the module of its speed does not change. But speed is a vector magnitude, and it is characterized not only by a numerical value, but also the direction. With a uniform movement around the circle, the direction of the velocity vector changes. Therefore, such a uniform movement is accelerated.

Linear speed:;

Linear and angular velocity are associated with the relation:

Centripetal acceleration :;

Corner speed:;

Slide 14. (Working with illustrations on the slide)

Direction of velocity vector.Linear (instantaneous speed) is always aimed at a tangent of the trajectory spent on that point where the physical body is currently located.

The velocity vector is aimed at the tangent of the described circle.

Uniform body movement around the circle is a movement with acceleration. With the uniform movement of the body along the circumference, υ and ω remain unchanged. In this case, when moving, only the direction of the vector changes.

Slide 15. Centripetal force.

The force holding the rotating body on the circle and directed towards the center of rotation is called the centripetal force.

To obtain a formula for calculating the magnitude of the centripetal force, you need to use the second Newton law, which is applicable to any curvilinear movement.

Substituting in the formula The value of the centripetal accelerationa. c. = , we obtain the centripetal force formula:

F \u003d.

From the first formula, it is clear that with the same speed, the less the radius of the circle, the greater the centripetal force. So, on the turns of the road to the moving body (train, car, bike) should act towards the center of the roundabout, the greater force than the cooler turn, that is, the smaller the radius radius.

The centripetal force depends on the linear speed: it increases with increasing speed. It is well known to all skaters, skiers and cyclists: than with greater speed Move, the harder to make a turn. The chasters know very well how dangerously cool turn the car at high speed.

Slide 16.

Summary Table physical quantitiescharacterizing curvilinear movement (analysis of dependencies between values \u200b\u200band formulas)

Slides 17, 18, 19. Examples Movement around the circle.

Circular motion on the roads. Movement of satellites around the earth.

Slide 20. Amusement, carousel.

Pupil message 3. In the Middle Ages by carousels (the word then had male Rod) Changed knight tournaments. Later, in the XVIII century, to prepare for tournaments, instead of kits with real rivals, began to use a rotating platform, a model of modern entertainment carousel, which at the same time appeared at city fairs.

In Russia, the first carousel was built on June 16, 1766 in front of the Winter Palace. The carousel consisted of four cadry: Slavic, Roman, Indian, Turkish. The second time the carousel was built in the same place, in the same year on July 11th. Detailed description These carousels are given in the newspaper St. Petersburg Vedomosti 1766.

Carousel, common in the courtyards in soviet time. The carousel can be driven by both the engine (usually electric) and the forces of the spinners themselves, which before sitting on the carousel, spin it. Such carousels that need to be unwritten by the riding themselves are often installed on children's playgrounds.

In addition to attractions, carousels are often called other mechanisms that have similar behavior - for example, in automated lines on spilling beverages, packaging of bulk substances or production of printed products.

In the figurative sense, the carousel call a series of quickly changing objects or events.

18 min

Fastening a new material. The use of knowledge and skills in the new situation.

Teacher. Today in this lesson we met with a description of the curvilinear movement, with new concepts and new physical quantities.

Conversation on questions:

What is the period? What is the frequency? How are these values \u200b\u200brelated to each other? What units are measured? How can they determine?

What is the angular speed? What units is it measured? How can I calculate it?

What are the angular speed? What is the unit of angular speed?

How are the angular and linear body movement speeds?

How is the centripetal acceleration? What formula is it calculated?

Slide 21.

Exercise 1. Fill in the table by solving the tasks on the source data (Fig. 2), then we will verify the answers. (Students work independently with a table, you need to prepare a printout of a table for each student in advance)

Fig.2

Slide 22. Task 2.(orally)

Pay attention to the animation effects of the drawing. Compare the characteristics of the uniform movement of the blue and red ball. (Working with a slide).

Slide 23. Task 3.(orally)

The wheels of the presented modes of transport for the same time make an equal number of revolutions. Compare their centripetal acceleration.(Working with Slide Materials)

(Work in the group, conducting an experiment, printing instructions for the experiment is on each table)

Equipment: Stopwatch, ruler, ball, pinned on the thread, tripod with a clutch and a paw.

Purpose: explorethe dependence of the period, frequency and acceleration from the rotational radius.

Work plan

Measure Time T 10 full revolutions of the rotational motion and the radius R rotation, the ball fixed on the thread in the tripod.

Calculate The period T and frequency, speed of rotation, centripetal acceleration Results Substitute as a task.

Change Radiation radius (thread length), repeat the experience another 1 time, trying to keep the previous speed,applying former effort.

Take output On the dependence of the period, frequency and acceleration from the rotational radius (the lower the rotation radius, the less the period of circulation and more frequency value).

Slides 24 -29.

Front work with interactive test.

You must select one answer out of three possible if the correct answer was chosen, then it remains on the slide, and the green indicator begins to flash, the wrong answers disappear.

The body moves around the circumference with a constant modulo speed. How will its centripetal acceleration change with a decrease in the circle radius 3 times?

In the centrifuge washing machine, underwear during annealing is moving around the circle with a constant speed in the horizontal plane. How does the vector of its acceleration are directed?

The skater is moving at a speed of 10 m / s around the circumference with a radius of 20 m. Determine its centripetal acceleration.

Where is the acceleration of the body when it is driving around the circle with a constant speed of the speed?

The material point moves around the circumference with constant modulo speed. How will the module of its centripetal acceleration change if the speed of the point is tripled three?

The wheel of the machine makes 20 revolutions for 10 s. Determine the wheel circulation period?

Slide 30. Solving tasks(independent work in the presence of time in class)

Option 1.

With which period should be rotated with a radius of 6.4 m to rotate so that the centripetal acceleration of the person on the carousel was equal to 10 m / s 2 ?

In the circus arena, the horse jumps at such a speed that 2 times cut 2 minutes. The radius of the arena is equal to 6.5 m. Determine the period and speed, speed and centripetal acceleration.

Option 2.

Rounding frequency 0.05 C -1 . A man rotating the carousel is at a distance of 4 m from the axis of rotation. Determine the centripetal acceleration of a person, the period of circulation and the angular velocity of the carousel.

Bicycle wheel rim point makes one turn for 2 s. Radius wheel 35 cm. What is the centripetal acceleration of the wheel of the wheel?

18 min

Summing up the lesson.

Estimation. Reflection.

Slide 31. .

D / s: p. 18-19, Exhibit 198 (2.4).

http.:// www. stmary.. wS./ highschool/ physics./ hOME./ lab/ labgraphic. gIF.

1. Alternate Movement around the circle

2. Current speed of rotational motion.

3. Rotation performance.

4.Prust of rotation.

5. Linear speed with corner.

6.centreter acceleration.

7. Eranted movement around the circumference.

8. Harl acceleration in the equalized movement around the circle.

9. Tangential acceleration.

10. Zakon equal to the circumference in the circumference.

11. The average angular velocity in an equilibrium movement around the circumference.

12.Formulas establishing a link between angular velocity, angular acceleration and angle of rotation in an equilibrium movement around the circle.

1.Uniform Movement around the circle - movement in which material point During equal intervals, equal segments of the circumference arc passes, i.e. The point moves around the circumference with constant modulo speed. In this case, the rate is equal to the attitude of the arc of the circle passing the point to the time of movement, i.e.

and is called the linear speed of the circumference.

As in curvilinear movement, the velocity vector is aimed at tangent to the circumference in the direction of movement (Fig.25).

2. Corner speed in uniform movement around the circle - The ratio of the rotation of the radius by the time of rotation:

In uniform movement around the circle, the angular speed is constant. In the system C, the angular speed is measured in (rad / c). One radian is pleased with the central angle, tightening the circumference arc with a radius equal. The full angle contains radians, i.e. In one turn, the radius turns to the angle of radians.

3. Rotation period - The time interval T, during which the material point makes one full turn. In the system system, the period is measured in seconds.

4. Rotation frequency - The number of revolutions committed in one second. In the system, the frequency is measured in hertz (1Hz \u003d 1). One hertz - the frequency at which one revolution is performed in one second. Easy to figure out that

If, during T, the point performs N revolutions around the circumference.

Knowing the period and speed of rotation, the angular velocity can be calculated by the formula:

5 Linear speed connection with corner. The length of the circumference arc is where the central angle, expressed in radians, tightening the arc of the circle radius. Now the linear speed is recorded in the form

It is often convenient to use formulas: or angular speed is often called cyclic frequency, and the frequency is a linear frequency.

6. Centripetal acceleration. In a uniform movement around the circle, the velocity module remains unchanged, and its direction is continuously changing (Fig.26). This means that the body moving evenly around the circumference is experiencing acceleration, which is directed to the center and is called the centripetal acceleration.

Let the arc of the circle passed over the interval of time. We transfer the vector, leaving it parallel to myself so that its beginning coincides with the beginning of the vector at the point V. The speed change module is equal, and the centripetal acceleration module is equal to

In Fig. 26, the triangles of AOs and the FROS are equally shared and corners at the vertices of O and B are equal, as angles with mutually perpendicular sides of the AO and OV, it means that the triangles of AOs and the internal combustion system are like. Consequently, if that is, the time interval takes how small values \u200b\u200btakes place, then the arc can be approximately considered to be equal to chord AV, i.e. . Therefore, we can write down given that the VD \u003d, OA \u003d R will be obtained by both parts of the last equality on, we obtain the expression for the centripetal acceleration module in a uniform movement around the circle :. Given that we obtain two frequently used formulas:

So, in a uniform movement around the circle, the centripetal acceleration is constantly in the module.

It is easy to figure out that in the limit when, angle. This means that the angles at the base of the DS triangle of the DVS are striving by the value, and the velocity change vector becomes perpendicular to the velocity vector, i.e. Directed along the radius to the center of the circle.

7. Equipment of the circle - Movement around the circle, in which for equal intervals of the time, the angular speed changes to the same magnitude.

8. Angular acceleration in the equalized movement around the circle - the ratio of changes in the angular velocity by the time interval, during which this change occurred, i.e.

where the initial value of the angular velocity, the final value of the angular velocity, the angular acceleration, is measured in the SI system. From the last equality we obtain the formula for calculating the angular velocity

And if .

Multiplying both parts of these equalities to and considering that - tangential acceleration, i.e. Acceleration aimed at a tangent of circumference, we obtain formula for calculating linear speed:

And if .

9. Tangential acceleration Nutally equal to changing the speed per unit of time and is directed along the tangent to the circumference. If\u003e 0,\u003e 0, then the movement is equivalent. If a<0 и <0 – движение.

10. The law of equivalent movement in the circumference. The path traveled around the circumference in the equal token movement is calculated by the formula:

Substituting here, reducing on, we obtain the law of equal casting in the circumference:

Or, if.

If the movement is equivalent, i.e.<0, то

11.Full acceleration in equivalent movement around the circle. In an equilibrium movement around the circle, the centripetal acceleration increases over time, because Thanks to tangential acceleration, linear speed increases. Very often, the centripetal acceleration is called normal and referred to as. Since total acceleration is currently determined by the Pythagoreo Theorem (Fig. 27).

12. Average angular speed in an equilibrium movement around the circle. The average linear speed in an equilibrium movement around the circle is equal to. Substituting here and and reducing to get

If, then.

12. Formulas that establish the relationship between angular velocity, an angular acceleration and an angle of rotation in an equilibrium movement around the circle.

Substituting in the formula of the magnitude ,,,

and cutting on, get

Lecture- 4. Dynamics.

1. Dynamics

2. Interaction tel.

3. Inertia. The principle of inertia.

4. The first law of Newton.

5. Free material point.

6. Inertial reference system.

7. Neinercial reference system.

8. The principle of relativity of Galilee.

9. Transformation of Galilee.

11. Addition of forces.

13. The density of substances.

14. Center of Mass.

15. The Second Law of Newton.

16. Force measurement unit.

17. The Third Newton Law

1. Dynamics There is a section of mechanics studying a mechanical movement, depending on the forces causing a change in this movement.

2.Tel interactions. Bodies may be embedded as with direct contact contact, and at a distance through a special type of matter called the physical field.

For example, all bodies are attracted to each other and this attraction is carried out by means of a gravitational field, and attraction forces are called gravitational.

The bodies carrying an electric charge interact through the electric field. Electrical currents interact through a magnetic field. These forces are called electromagnetic.

Elementary particles interact through nuclear fields and these forces are called nuclear.

3.Intery. In IV century BC e. The Greek philosopher Aristotle argued that the cause of the body movement is the force acting on the other body or tel. At the same time, according to the movement of the opinion of Aristotle, constant force reports the body constant speed and movement ceases to stop the action.

In the 16th century Italian physicist Galileo Galilee, conducting experiments with bodies rolling through the inclined plane and with falling bodies showed that the constant power (in this case the body weight) informs the body acceleration.

So, on the basis of experiments, Galilee showed that the power is caused by accelerating tel. We give the reasoning of Galilee. Let a very smooth ball rolling along a smooth horizontal plane. If the ball does not interfere with anything, he can roll for how long. If you pour out a thin layer of sand on the path of the ball, then it will stop very soon, because He was affected by the power of sand friction.

So Galilee came to the formulation of the principle of inertia, according to which the material body retains the state of rest or uniform straight movement, if external forces do not apply. Often, this property of matter is called inertia, and the movement of the body without external influence on the inertia.

4. First Law Newton. In 1687, based on the principle of inertia, Galilee Newton formulated the first law of dynamics - the first law of Newton:

The material point (body) is at rest or uniform rectilinear movement, if other bodies do not act on it, or the forces acting from other bodies are balanced, i.e. Compacted.

5.Free material point - The material point on which other bodies do not work. Sometimes they say - isolated material dot.

6. Inertial reference system (ISO) - The reference system relative to which the isolated material point moves straight and evenly, or is at rest.

Any reference system that moves uniformly and straightly relative to ISO is inertial,

We give another formulation of the first law of Newton: there are reference systems relative to which the free material point moves straight and evenly, or is at rest. Such reference systems are called inertial. Often, the first Newton law is called the law of inertia.

The first law of Newton can also be given such a wording: any material body resists changing its speed. This property of matter is called inertia.

With the manifestation of this law, we are confronted daily in urban transport. When the bus sharply picks up speed, we pressed to the back of the seating. When the bus slows down, our body lies along the movement of the bus.

7. Non-inertial reference system -the reference system that moves unevenly relative to ISO.

The body, which relative to ISO is at rest or uniform rectilinear movement. Regarding non-inertial reference system moves unevenly.

Any rotating reference system is the non-inertial reference system, because In this system, the body has a centripetal acceleration.

In nature and technology there are no bodies that could serve as ISO. For example, the Earth rotates around its axis and any body on its surface is experiencing a centripetal acceleration. However, for rather short periods of time, the reference system associated with the surface of the Earth in some approximation can be considered an ISO.

8.The principle of relativity of Galilee.ISO can be a lot of salt. Therefore, the question arises: what do the same mechanical phenomena in different ISO look like? It is possible if using mechanical phenomena, detect the ISO movement in which they are observed.

The answer to these questions gives the principle of relating classical mechanics, open with Galileem.

The meaning of the principle of relativity of classical mechanics is to approval: all mechanical phenomena proceed exactly equally in all inertial reference systems.

This principle can be formulated and so: all laws of classical mechanics are expressed by the same mathematical formulas. In other words, no mechanical experiences will help us discover the ISO movement. This means that an attempt to detect the ISO movement is deprived of meaning.

With the manifestation of the principle of relativity, we encountered, followed by trains. At the moment when our train costs at the station, and the train standing in the next way slowly starts movement, then in the first moments it seems to us, our train is moving. But on the contrary, when our train smoothly picks up, it seems to us that the movement began a neighboring train.

In the example above, the principle of relativity is manifested during small time intervals. With increasing speed, we begin to feel the shock to rock the car, i.e., our reference system becomes non-inertial.

So, an attempt to detect the ISO movement is deprived of meaning. Therefore, it is absolutely indifferent, which ISO is considered a fixed, and which - moving.

9. Transformation Galilee.. Let two ISO and moving relative to each other at speed. According to the principle of relativity, we can put that ISO is fixed, and ISO is moving relative at speeds. For simplicity, we assume that the corresponding axes of the coordinates of systems and are parallel, and the axes are coincided. Let at the time of the start of the systems coincide and the movement occurs along the axes and, i.e. (Fig.28)

11. Addition of power. If the particle is applied two forces, then the resulting force is equal to their vector, i.e. The diagonal of the parallelogram built in vectors and (Fig.29).

The same rule with the decomposition of this force into two components. To do this, on the vector of this force, as a diagonal is built by parallelograms, the sides of which coincide with the direction of the components applied to this particle.

If several forces are applied to the particle, then the resulting equal to the geometric sum of all forces:

12.Weight. Experience has shown that the relation of the force module to the acceleration module, which this force reports the body, is the value constant for this body and is called a body weight:

From the last equality it follows that the greater the mass of the body, the most power must be attached to change its speed. Consequently, the greater the mass of the body with the more inert, i.e. Mass is a measure of inertness tel. The mass is thus defined in the inert mass.

In the system, the mass is measured in kilograms (kg). One kilogram is a mass of discallive water in the volume of one cubic decimeter taken at temperatures.

13. Density of substance - Mass of a substance contained in a unit of volume or the ratio of body weight to its volume

The density is measured in () in the SI system. Knowing the body density and its volume can be calculated by its mass by the formula. Knowing density and body weight, its volume is calculated by the formula.

14.Center Mass. - The point of the body, which has the property that, if the direction of force passes through this point the body moves properly. If the direction of action does not pass through the center of the masses, the body moves, simultaneously rotating around his center

15. Second Newton Law. In ISO, the sum of the forces acting on the body is equal to the product of the body mass on the acceleration reported to this force

16.Unit measurement unit. In the system, the force is measured in Newton. One Newton (N) is a force that acting on a body weighing one kilogram informs him acceleration. Therefore .

17. Third Law Newton. Forces with which two bodies act on each other are equal to the module, opposite to the direction and act along one straight line connecting these bodies.

Since the linear speed evenly changes the direction, then the circle movement cannot be called uniform, it is equivalent.

Angular velocity

Period and frequency

Rotation period T. - This is the time for which the body makes one turn.

Rotation frequency is the number of revolutions in one second.

Frequency and period are interconnected by the ratio

Communication with angular speed

Line speed

Each point on the circle moves at some speed. This speed is called linear. The direction of the linear velocity vector always coincides with the tangent of the circumference. For example, sparks from under the grinding machine are moving, repeating the direction of instantaneous speed.

Consider the point on the circle that makes one turn, the time that spent is a period T.. The path that overcomes the point is the length of the circle.

Centripetal acceleration

When driving around the circle, the acceleration vector is always perpendicular to the velocity vector, directed to the center of the circle.

Using previous formulas, you can derive the following ratios

The law of addition of speeds is valid for both rotational motion. If the movement of the body or reference system is not uniform, the law is used for instantaneous speeds. For example, the speed of a person walking along the edge of the rotating carousel is equal to the vector sum of the linear speed of rotation of the edge of the carousel and the speed of the human movement.

According to Newton's second law, the cause of any acceleration is power. If the moving body is experiencing a centripetal acceleration, the nature of the forces, the action of which caused by this acceleration, may be different. For example, if the body moves around the circumference on a rope attached to it, then the active force is the force of elasticity.

If the body lying on the disk rotates with the disk around its axis, then the force of friction is such force. If the power stops its action, then the body will move in a straight line

Consider moving the point on the circle from A in B. Linear speed is equal v A. and v B. respectively. Acceleration - Changing the speed per unit of time. Find the difference of vectors.