Every action has a reaction, Newton's law. Laws of karma: for every action we take, the Universe has a certain reaction. Interaction of two bodies

We will try to consider one of the basic laws of the Universe - the law of karma, or, as it is called in the scientific world, the law of cause and effect.

We will try to consider one of the basic laws of the Universe - the law of karma, or, as it is called in the scientific world, the law of cause and effect. Even a schoolchild can formulate it briefly: every action has a reaction.

The Vedas say the same thing: “For every action of ours, be it a thought, a feeling, a word or a physical action, the Universe has a certain reaction, and the reward - whether it is punishment or punishment - depends on the action.

And if in ordinary life a person may never receive reward or punishment from the government, the judiciary, or the people around him - since they themselves are under the influence of this law, then at the universal level the Creator himself monitors the observance of this law. “Not even a blade of grass moves without the will of God.” It is the law of karma that shapes a person’s destiny.

What is fate and where does it come from? I hope that every reader has thought about the questions: “Who am I? Why was I born in this place and in this family?”, “What is the meaning of my life?”, “Why am I suffering?” - it is with these questions that truly human life begins. If a person thinks only about how to eat, sleep, copulate and protect himself, then he is no different from an animal. Every person has a destiny - a baby is born, and he has a life line, there is a natal chart that allows you to easily determine the main milestones of destiny.

I remember how in March 1994 I visited a small town near Madras (South India), where in the Vishnu temple two brahmans (priests, clergymen), looking at the Rashi (natal chart made according to the Indian system) and on the lines on their hands, told you your destiny: who you are, what country you are from, how your childhood was, what your family and financial situation is, what awaits you, etc., etc. - with an accuracy of 90 percent. And by and large, it's not that difficult. In my courses, students after just a few months of training can say, for example, how a person’s family life will turn out in this incarnation.

There are a lot of great people (and not great people, by the way, either) who had their fate predicted in childhood: these are Alexander the Great, A.S. Pushkin, President Kennedy and others. Everyone also knows that at all times there were great seers, such as Vanga and Nostradamus, who predicted the future with great accuracy. All this completely refutes the views of those scientists who believe that everything in this world is random. But a future that is predicted with an accuracy of at least a few percent is no longer accidental.

This also, to put it mildly, complements modern Christian doctrine (I emphasize: modern, since for the first three hundred years Christians believed in reincarnation. And only at one of the first ecumenical councils was the treatise on the transmigration of the soul excluded - this is a historical fact).

Ask any Christian preacher: “Why are there children who die a hard death, and where do they go?”, “Why is one born into a family of a millionaire and does not know what illness is, and someone is born into a poor family and suffers all his life? "

But if we accept the concept of transmigration of souls and the law of karma, then everything will fall into place. After all, we also receive doctors in accordance with our destiny. I am literally writing this article while my daughter is undergoing surgery. The operation is very serious, only a heart transplant is more difficult.

And this also once again reminds me of the law of karma. Six years ago, well-known Vedic astrologers in Moscow, analyzing my life and karmic tasks (we have a rule that we “lead” each other), told me that in a previous life I had done such and such, and In this one, I will have a girl with a heart condition. And I had no choice but to admit that she had already been born. And although all the doctors said with one voice that she would live for a maximum of 3-4 years, I, knowing her fate, had a different opinion. And at this stage (as, indeed, before and in the future), she lives in accordance with fate and the Higher Will, and not in accordance with the opinion of doctors, as, indeed, each of us.

Classification of karma - from primary sources. Now I would like to give a description of the law of karma - just or almost as it was given directly in the primary sources in the Vedas. Since now the word “karma” is known, and different people, pronouncing it, put different meanings into it. There are many karma “specialists” who claim that they can “clean” your karma, without knowing what is meant by the word “karma”. Karma means "action" (Sanskrit). It includes the following concepts

• sanchita - karma accumulated in previous lives;

prarabdha - part of the accumulated karma, determined for the current incarnation;

kriyaman - karma created by us in this life;

• agami - karma of future incarnations, if the current one is not the last.

There is also vikarma, which includes:

anti-parental karma;

• anti-family karma;

antisocial karma;

• anti-human karma.

Akarma: One who has reached a certain level of love for God no longer has duties, but his karma remains. You can achieve akarma by doing your activities with complete detachment, without striving for results, with love. The results of these types of karma are different:

• akarma leads to salvation;

vikarma - to punishment from above, a series of terrible incarnations and endless suffering;

• karma can lead to akarma and vikarma.

The akarma element leads to salvation and the vikarma element leads to bondage. Karma thus contains four elements. Let's explain them in more detail. Sanchita karma is the total cumulative remainder of karma. Only man produces karma, while animals are in the state of Bhoga-Yoni, in which they can only suffer or rejoice and can neither create nor eliminate karma, as people do.

Sanchita karma is the karma created by a person in his previous human incarnations. And prarabdha is part of sanchita, determined for this incarnation. She has both a positive and a negative side. Human joys and achievements stem from its positive side, and misfortunes and losses stem from its negative side. Another part of sanchita can be described as previously created urges that can enter the present life at any moment. And when people unexpectedly do something that they least expected, it may be the result of just such an impulse.

Therefore, human life is a story of prarabdha and urges for which there is no sound explanation in terms of heredity and environmental influences. The behavior of an individual is thus shaped by four factors: environment and heredity, prarabdha and motivations that have their source in a previous life. Kriyaman karma is an area in which a person can improve or ruin his destiny. Only in this rather limited area can he enjoy freedom of action. Although the motivations of the previous life and prarabdha often create conflicts. The best advice that all great yogis give to people is to consciously experience (experience) prarabdha. And do good deeds in the field of kriyaman. That is, to humbly and patiently accept what cannot be prevented, and in the field of free will to perform actions that bring us closer to akarma, the transcendental level.

Karma and health. Having talked about fate and karma, we absolutely do not want the reader to have a fatalistic mood. “Why get treatment if everything is predetermined?” Well, firstly, not everything - there is always a certain freedom of choice. Secondly, Ayurveda says that one must begin to fight diseases, fires and debts immediately, making every effort. Thirdly, according to Vedic astrology and Ayurveda, as well as a huge variety of other sources, we are on the threshold of a new era (golden age, age of Aquarius, etc.) and the pace of our lives is now accelerating both on the external level and on the inside. And if earlier it took several lives to work out or solve any karmic problem, now it can be solved in one life, or even in several years.

But, unfortunately, the opposite is also true. Now, more than ever, the wrong worldview, resentment, anger, fear for the future, etc. are dangerous, and a person can be twisted very quickly, without even letting him understand: “Why?!” It is now more important than ever to be guided by love, forgiveness, and tolerance if you want your life to be long and healthy. According to studies, people who live a long time believe in God, adhere to vegetarianism, live in environmentally friendly places, eat right, use the services of modern medicine, etc.

But there are also long-livers who do not comply with any of the above conditions. And what unites them? This is love, kindness, patience and a good sense of humor. No one has ever seen or heard of a touchy, hysterical woman living a long time without getting sick. Just like aggressive, irritable, restless people. That is, our happiness and health, as well as those around us, are greatly influenced by our character and worldview.

By the way, you can find evidence of the above not only from the sages - the saints of India and Tibet, but also from many of our contemporaries. In particular, Edgar Cayce (you can download the book by Kevin J. Todeschi. “Edgar Cayce and the Akashic Records” in our library), a man who predicted many events with great accuracy. But the most important thing is that he could find the origin of every disease in past lives.

Ninety thousand such cases have been registered in the institute named after this great American. There are other important studies in this area, but we are not able to list them all. But there will be more and more such research, and diseases will be defeated not by the discovery of new medications, but by changing people’s consciousness! So let's enter the new century with a clean mind and a healthy body! published

When no forces act on them (or mutually balanced forces act on them), they are in a state of rest or uniform linear motion.

Historical formulation

Modern formulation

Where p → = m v → (\displaystyle (\vec (p))=m(\vec (v)))- point impulse, v → (\displaystyle (\vec (v)))- its speed, and t (\displaystyle t)- time . With this formulation, as with the previous one, it is believed that the mass of a material point is constant in time.

Attempts are sometimes made to extend the scope of the equation d p ​​→ d t = F → (\displaystyle (\frac (d(\vec (p)))(dt))=(\vec (F))) and in the case of bodies of variable mass. However, along with such a broad interpretation of the equation, it is necessary to significantly modify previously accepted definitions and change the meaning of such fundamental concepts as material point, momentum and force .

Notes

When several forces act on a material point, taking into account the principle of superposition, Newton’s second law is written as:

Newton's second law, like all classical mechanics, is valid only for the movement of bodies at speeds much lower than the speed of light. When bodies move at speeds close to the speed of light, a relativistic generalization of the second law is used, obtained within the framework of the special theory of relativity.

It should be taken into account that it is impossible to consider a special case (when F → = 0 (\displaystyle (\vec (F))=0)) of the second law as an equivalent of the first, since the first law postulates the existence of ISO, and the second is formulated already in ISO.

Historical formulation

Newton's original formulation:

Newton's third law

This law describes how two material points interact. Let there be a closed system consisting of two material points, in which the first point can act on the second with a certain force, and the second on the first with a force. Newton's third law states: force of action F → 1 → 2 (\displaystyle (\vec (F))_(1\to 2)) equal in magnitude and opposite in direction to the counterforce F → 2 → 1 (\displaystyle (\vec (F))_(2\to 1)).

Newton's third law is a consequence of the homogeneity, isotropy and mirror symmetry of space.

Newton's third law, like the other laws of Newtonian dynamics, gives practically correct results only when the velocities of all bodies in the system under consideration are negligible compared to the speed of propagation of interactions (the speed of light).

Modern formulation

The law states that forces arise only in pairs, and any force acting on a body has a source of origin in the form of another body. In other words, strength is always the result interactions tel. The existence of forces that arise independently, without interacting bodies, is impossible.

Historical formulation

Newton gave the following formulation of the law:

Consequences of Newton's laws

Newton's laws are axioms of classical Newtonian mechanics. From these, as a consequence, the equations of motion of mechanical systems are derived, as well as the “conservation laws” indicated below. Of course, there are also laws (for example, universal gravitation or Hooke’s) that do not follow from Newton’s three postulates.

Equations of motion

The equation F → = m a → (\displaystyle (\vec (F))=m(\vec (a))) is a differential equation: acceleration is the second derivative of the coordinate with respect to time. This means that the evolution (movement) of a mechanical system in time can be unambiguously determined if its initial coordinates and initial velocities are specified.

Note that if the equations describing our world were first-order equations, then such phenomena as inertia, oscillations, and waves would disappear from our world.

Law of conservation of momentum

The law of conservation of momentum states that the vector sum of the impulses of all bodies of the system is a constant value if the vector sum of external forces acting on the system of bodies is equal to zero.

Law of conservation of mechanical energy

Newton's laws and inertial forces

The use of Newton's laws involves specifying a certain ISO. However, in practice we have to deal with non-inertial reference systems. In these cases, in addition to the forces discussed in Newton’s second and third laws, mechanics introduces the so-called inertia forces.

Usually we are talking about two different types of inertial forces. The force of the first type (D'Alembert inertial force) is a vector quantity equal to the product of the mass of a material point and its acceleration, taken with a minus sign. Forces of the second type (Eulerian inertia forces) are used to obtain the formal possibility of writing the equations of motion of bodies in non-inertial reference systems in a form that coincides with the form of Newton’s second law. By definition, the Euler inertial force is equal to the product of the mass of a material point and the difference between the values ​​of its acceleration in the non-inertial reference frame for which this force is introduced, on the one hand, and in some inertial reference frame, on the other. The inertial forces defined in this way are not forces in the true sense of the word; they are called fictitious , apparent or pseudo-forces .

Newton's laws in the logic of a mechanics course

There are methodologically different ways of formulating classical mechanics, that is, choosing its fundamental postulates, on the basis of which the corollary laws and equations of motion are then derived. Giving Newton's laws the status of axioms based on empirical material is only one of these methods (“Newtonian mechanics”). This approach is accepted in high school, as well as in most university general physics courses.

An alternative approach, used primarily in theoretical physics courses, is Lagrangian mechanics. Within the framework of the Lagrangian formalism, there is one and only formula (recording the action) and one and only postulate (bodies move so that the action is stationary), which is a theoretical concept. From this we can derive all Newton's laws, although only for Lagrangian systems (in particular, for conservative systems). It should be noted, however, that all known fundamental interactions are described precisely by Lagrangian systems. Moreover, within the framework of the Lagrangian formalism, one can easily consider hypothetical situations in which the action has some other form. In this case, the equations of motion will no longer be similar to Newton’s laws, but classical mechanics itself will still be applicable.

Historical sketch

The practice of using machines in the manufacturing industry, building construction, shipbuilding, and the use of artillery allowed, by Newton's time, to accumulate a large number of observations on mechanical processes. The concepts of inertia, force, and acceleration became increasingly clear during the 17th century. The works of Galileo, Borelli, Descartes, and Huygens on mechanics already contained all the necessary theoretical prerequisites for Newton to create a logical and consistent system of definitions and theorems in mechanics.

Original text (Latin)

LEX I
Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quantenus a viribus impressis cogitur statum illum mutare.

LEX II
Mutationem motus proportionalem esse vi motrici impressae et fieri secundum lineam rectam qua vis illa imprimitur.

Actioni contrariam semper et aequalem esse reactionem: sive corporum duorum actiones in se mutuo semper esse aequales et in partes contrarias dirigi.

For the Russian translation of these laws, see the previous sections.

Newton also gave strict definitions of such physical concepts as momentum(not quite clearly used by Descartes) and force. He introduced into physics the concept of mass as a measure of the inertia of a body and, at the same time, its gravitational properties (previously, physicists used the concept weight).

In the middle of the 17th century, the modern technology of differential and integral calculus did not yet exist. The corresponding mathematical apparatus in the 1680s was simultaneously created by Newton himself (1642-1727), as well as by Leibniz (1646-1716). Euler (1707-1783) and Lagrange (1736-1813) completed the mathematization of the fundamentals of mechanics.

Notes

1. Isaac Newton. Mathematical principles of natural philosophy. Translation from Latin and notes by A. N. Krylov / ed. Polaka L.S. - M.: Nauka, 1989. - P. 40-41. - 690 s. - (Classics of science). - 5,000 copies. - ISBN 5-02-000747-1.
2. Targ S. M. Newton's laws of mechanics// Physical encyclopedia: [in 5 volumes] / Ch. ed. A. M. Prokhorov. - M.: Great Russian Encyclopedia, 1992. - T. 3: Magnetoplasma - Poynting’s theorem. - P. 370. - 672 p. - 48,000 copies. - ISBN 5-85270-019-3.
3. Inertia// Physical encyclopedia / Ch. ed. A. M. Prokhorov. - M.: Soviet Encyclopedia, 1990. - T. 2. - P. 146. - 704 p. - ISBN 5-85270-061-4.
4. Inertial reference frame// Physical encyclopedia (in 5 volumes) / Edited by academician. A. M. Prokhorova. - M.: Soviet Encyclopedia, 1988. - T. 2. - P. 145. - ISBN 5-85270-034-7.
5. “An additional characteristic (compared to the geometric characteristics) of a material point is the scalar quantity m - the mass of the material point, which, generally speaking, can be either a constant or a variable quantity. ... In classical Newtonian mechanics, a material point is usually modeled by a geometric point with an inherent constant mass) which is a measure of its inertia.” p. 137 Sedov L. I., Tsypkin A. G. Fundamentals of macroscopic theories of gravitation and electromagnetism. M: Nauka, 1989.
6. Markeev A.P. Theoretical mechanics. - M.: CheRO, 1999. - P. 87. - 572 p.“The mass of a material point is considered a constant value, independent of the circumstances of its movement.”
7. Golubev Yu. F. Fundamentals of theoretical mechanics. - M.: MSU, 2000. - P. 160. - 720 p. - ISBN 5-211-04244-1. « Axiom 3.3.1. The mass of a material point retains its value not only in time, but also during any interactions of the material point with other material points, regardless of their number and the nature of the interactions.”
8. Zhuravlev V. F. Fundamentals of theoretical mechanics. - M.: Fizmatlit, 2001. - P. 9. - 319 p. - ISBN 5-95052-041-3.“The mass [of a material point] is assumed to be constant, independent of either the position of the point in space or time.”
9. Markeev A.P. Theoretical mechanics. - M.: CheRO, 1999. - P. 254. - 572 p.“...Newton's second law is valid only for a point of constant composition. The dynamics of systems of variable composition require special consideration.”
10. “In Newtonian mechanics... m=const and dp/dt=ma.” Irodov I. E. Basic laws of mechanics. - M.: Higher School, 1985. - P. 41. - 248 p..
11. Kleppner D., Kolenkow R. J. An Introduction to Mechanics. - McGraw-Hill, 1973. - P. 112. - ISBN 0-07-035048-5.“For a particle in Newtonian mechanics, M is a constant and (d/dt)(M v) = M(d v/dt) = M a».
12. Sommerfeld A. Mechanics = Sommerfeld A. Mechanic. Zweite, revision auflage, 1944. - Izhevsk: Scientific Research Center "Regular and Chaotic Dynamics", 2001. - P. 45-46. - 368 p. - ISBN 5-93972-051-X.

In the school physics course, Newton's three laws are studied, which are the basis of classical mechanics. Today every schoolchild is familiar with them, but in the time of the great scientist such discoveries were considered revolutionary. Newton's laws will be briefly and clearly described below; they help not only to understand the basis of mechanics and the interaction of objects, but also help to write data as an equation.

For the first time, the three laws were described by Isaac Newton in his work “Mathematical Principles of Natural Philosophy” (1867), in which not only the scientist’s own conclusions were presented in detail, but all the knowledge on this topic discovered by other philosophers and mathematicians. Thus, the work became fundamental in the history of mechanics, and later physics. It examines the movement and interaction of massive bodies.

Interesting to know! Isaac Newton was not only a talented physicist, mathematician and astronomer, but was also considered a genius in mechanics. He served as President of the Royal Society of London.

Each statement illuminates one of the spheres of interaction and movement of objects in nature, although the appeal to them was somewhat abolished by Newton, and they were accepted as points without a specific size (mathematical).

It was this simplification that made it possible to ignore natural physical phenomena: air resistance, friction, temperature or other physical indicators of the object.

The data obtained could only be described in terms of time, mass or length. It is because of this that Newton's formulations provide only suitable but approximate values ​​that cannot be used to describe the exact response of large or shape-changing objects.

The movement of massive objects that participate in the definitions is usually calculated in inertial, presented in the form of a three-dimensional coordinate system, and at the same time it does not increase its speed and does not rotate around its axis.

It is often called Newton's frame of reference, but the scientist never created or used such a system, but used an irrational one. It is in this system that bodies can move as Newton describes it.

First Law

Called the law of inertia. There is no practical formula for it, but there are several formulations. Physics textbooks offer the following formulation of Newton's first law: there are inertial frames of reference in relation to which an object, if it is free from the influence of any forces (or they are instantly compensated), is at complete rest or moves in a straight line and with the same speed. What does this definition mean and how to understand it?

In simple words, Newton's first law is explained as follows: any body, if not touched or influenced in any way, will remain constantly at rest, that is, stand in place indefinitely. The same thing happens when it moves: it will move uniformly along a given path indefinitely until something acts on it.

A similar statement was voiced by Galileo Galilei, but he could not clarify and accurately describe this phenomenon. In this formulation, it is important to correctly understand what inertial frames of reference are. To put it in very simple words, this is the system in which the action of this definition is carried out.

You can see a huge variety of similar systems in the world if you watch the movement:

• trains on a given section at the same speed;
• Moons around the Earth;
• Ferris wheels in the park.

As an example, consider a certain parachutist who has already opened his parachute and is moving in a straight line and at the same time uniformly in relation to the surface of the Earth. Human movement will not stop until gravity is compensated by movement and air resistance. As soon as this resistance decreases, the attraction increases, which will lead to a change in the speed of the parachutist - his movement will become rectilinear and uniformly accelerated.

It is in relation to this formulation that there is an apple legend: Isaac was resting in the garden under an apple tree and reflecting on physical phenomena, when a ripe apple fell from the tree and fell into the grass. It was the even fall that forced the scientist to study this issue and ultimately come up with a scientific explanation for the movement of an object in a certain frame of reference.

Interesting to know! In addition to three phenomena in mechanics, Isaac Newton also explained the movement of the Moon as a satellite of the Earth, created the corpuscular theory of light and decomposed the rainbow into 7 colors.

Second Law

This scientific justification concerns not just the movement of objects in space, but their interaction with other objects and the results of this process.

The law states: the increase in the speed of an object with some constant mass in an inertial frame of reference is directly proportional to the force of impact and inversely proportional to the constant mass of the moving object.

Simply put, if there is a certain moving body whose mass does not change, and an external force suddenly begins to act on it, then it will begin to accelerate. But the acceleration rate will directly depend on the impact and inversely depend on the mass of the moving object.

For example, consider a snow globe that is rolling down a mountain. If the ball is pushed in the direction of movement, then the acceleration of the ball will depend on the power of the impact: the greater it is, the greater the acceleration. But, the greater the mass of a given ball, the less acceleration will be. This phenomenon is described by a formula that takes into account acceleration, or “a,” the resultant mass of all acting forces, or “F,” as well as the mass of the object itself, or “m”:

It should be clarified that this formula can only exist if the resultant of all forces is not less than and not equal to zero. The law applies only to bodies that move at speeds less than light.

Useful video: Newton's first and second laws

Third Law

Many have heard the expression: “For every action there is a reaction.” It is often used not only for general educational purposes, but also for educational purposes, explaining that for every force there is a greater one.

This formulation comes from another scientific statement of Isaac Newton, or rather his third law, which explains the interaction of various forces in nature with respect to any body.

Newton's third law has the following definition: objects influence each other with forces of the same nature (connecting the masses of objects and directed along a straight line), which are equal in their modules and at the same time directed in different directions. This formulation sounds quite complicated, but it is easy to explain the law in simple words: every force has its own reaction or equal force directed in the opposite direction.

It will be much easier to understand the meaning of the law if we take as an example a cannon from which cannonballs are fired. The cannon acts on the projectile with the same force that the projectile exerts on the cannon. Confirmation of this will be a slight movement of the gun back during the shot, which will confirm the impact of the cannonball on the gun. If we take as an example the same apple that falls to the ground, it will become clear that the apple and the earth influence each other with equal force.

The law also has a mathematical definition, which uses the force of the first body (F1) and the second (F2):

The minus sign indicates that the force vectors of two different bodies are directed in opposite directions. It is important to remember that these forces do not compensate each other, since they are directed relative to two bodies, and not one.

Useful video: Newton's 3 laws using a bicycle as an example

Conclusion

These laws of Newton are briefly and clearly necessary for every adult to know, since they are the basis of mechanics and operate in everyday life, despite the fact that these laws are not observed under all conditions. They became axioms in classical mechanics, and on their basis the equations of motion and energy (conservation of momentum and conservation of mechanical energy) were created.

In contact with

Newton's third law states: “For every action there is a reaction.” But this applies not only to physical phenomena - in fact, approximately the same thing happens in our lives. When we think, speak or perform any action, we activate a force that will respond to us in the same way.

1. The law of cause and effect.
Whatever we create in the Universe, it will always return it to us. Therefore, if we want to find love, true friendship and happiness, then first of all we ourselves must love our loved ones, be a true friend and make people happy.

2. The law of creation.
The key to the correct internal state is independence from the outside world. To achieve it, you need to be yourself and surround yourself with those people and those things that we really we love and want to see in our lives.

3. The law of humility.
We cannot change the situation until we accept it. And if we see only an enemy in someone, then this means that we ourselves are still not oriented to a higher level of existence.

4. The law of growth.
The main thing for us is that we ourselves change and grow, and not the people, cities or technologies around us, because the life and time allotted to us is all that we really have.

5. Law of responsibility.
Life is a mirror. When something goes wrong in it, it means that we ourselves have internal problems, so we must take responsibility for what is happening, rather than looking for someone to blame.

6. Law of connection.
Even if what we do seems insignificant to us, it is very important to do it, since everything in the Universe is interconnected. The first step cannot be more important than the last, and vice versa, since they are both necessary to complete the task.

7. Law of focus.
It is impossible to think about two things at the same time. If you concentrate in search of something important, for example, spiritual values, then there will be no room in your head for greed or anger.

8. Law of acceptance.
We truly understand and accept only what we have learned in practice. If we believe something is true, but are not ready to prove it, then we only have an opinion, not knowledge.

9. The law is here and now.
Digging into the past and obsessively dreaming about the future distracts us from what is happening in the present moment, and old patterns of behavior and old dreams prevent us from finding something new.

10. Law of change.
History will repeat itself until we learn lessons from it that will change our path, so we shouldn’t do the same thing every time and expect different results.

11. Law of patience and rewards.
Any reward requires an investment of work, and the true joy of life is to continue to work hard, knowing that sooner or later we will achieve our goal.

12. The law of meaning and inspiration.
We only get what we deserve, because the true value of something is equal to the energy and effort that we spent to get what we want. But only those who love to give can receive something inspiring.

Newton's laws of dynamics (classical dynamics) have a limited range of applicability. They are valid for macroscopic bodies moving at speeds much lower than the speed of light in vacuum.

Statement of Newton's first law (it is also known as the law of inertia):

Newton's first law There are such reference systems, called inertial ones, relative to which a body moves rectilinearly and uniformly if other bodies do not act on it or the action of these bodies is compensated.

In an inertial reference frame, a body moves uniformly and rectilinearly in the absence of forces acting on it.

Inertia The phenomenon of maintaining the speed of a body in the absence of external influences or when they are compensated is called inertia. Therefore, Newton's first law is called the law of inertia.

If the resultant of all forces acting on a given body is zero, then the body moves uniformly and rectilinearly or does not move at all. In reality, it is impossible to achieve zero resultant force. But you can neglect some actions and choose a part of the movement when the speed of the body does not change significantly.

The law of inertia was first formulated by Galileo Galilei (1632). Newton generalized Galileo's conclusions and included them among the fundamental laws of motion.

ISO inertial reference systems are reference systems in which Newton's 1st law is satisfied.

So, the reason for a change in the speed of movement of a body in an inertial frame of reference is always its interaction with other bodies. To quantitatively describe the motion of a body under the influence of other bodies, it is necessary to introduce two new physical quantities - inert body weight And force.

Weight

Mass is a property of a body that characterizes its inertia. Under the same influence from surrounding bodies, one body can quickly change its speed, while another, under the same conditions, can change much more slowly. It is customary to say that the second of these two bodies has greater inertia, or, in other words, the second body has greater mass.

If two bodies interact with each other, then as a result the speed of both bodies changes, i.e., in the process of interaction, both bodies acquire acceleration. The ratio of the accelerations of these two bodies turns out to be constant under any influence. In physics, it is accepted that the masses of interacting bodies are inversely proportional to the accelerations acquired by the bodies as a result of their interaction.

Comparison of the masses of two bodies.

\[ \dfrac(m_1)(m_2) =-\dfrac(a_2)(a_1) \]

In this relationship, the quantities \(a_1\) and \(a_2\) should be considered as projections of the vectors \(a_1\) and \(a_2\) onto the OX axis. The minus sign on the right side of the formula means that the accelerations of the interacting bodies are directed in opposite directions.

In the International System of Units (SI), body mass is measured in kilograms (kg).

The mass of any body can be determined experimentally by comparison with standard mass (\(m_(\text(fl)) = 1 \text(kg)\)). Let \(m_1 = m_(\text(fl)) = 1 \text(kg)\). Then

\[ m_2=-\dfrac(a_1)(a_2) m_(\text(et)) \]

Body mass - scalar quantity. Experience shows that if two bodies with masses \(m_1\) and \(m_2\) are combined into one, then the mass \(m\) of the composite body turns out to be equal to the sum of the masses \(m_1\) and \(m_2\) of these bodies :

\[ M = m_1 + m_2 \]

This property of masses is called additivity.

Force

Force is a quantitative measure of the interaction of bodies. Force causes a change in the speed of a body. In Newtonian mechanics, forces can have a different physical nature: friction force, gravity force, elastic force, etc. Force is vector quantity, has a module, direction and point of application.

The vector sum of all forces acting on a body is called resultant force.

To change the speed of a body, it must be acted upon with some force. Naturally, the result of the action of forces of equal magnitude on different bodies will be different.

There are 4 main types interactions:

• gravitational,
• electromagnetic,
• strong,
• weak.

All interactions are manifestations of these basic types.

Examples of forces: gravity, elastic force, body weight, friction force, buoyant (Archimedean) force, lifting force.

What is strength? Force is a measure of the influence of one body on another.

Force is a vector quantity. Strength is characterized by:

• module (absolute value);
• direction;
• point application.

To measure forces it is necessary to set standard of strength And comparison method other forces with this standard.

As a standard of force, we can take a spring stretched to a certain specified length. Force module F 0, with which this spring, at a fixed tension, acts on the body attached to it is called standard of strength. The method of comparing other forces with the standard is as follows: if the body under the action of the measured force \(\vec(F)\) and the reference force \(\vec(F_0)\) remains at rest (or moves uniformly and rectilinearly), then the forces are equal in modulus \(\vec(F) \) = \(\vec(F_0) \) .

Comparison of force \(\vec(F)\) with the standard. \(\vec(F) \) = \(\vec(F_0 ) \)

If the measured force \(\vec(F ) \) is greater (in absolute value) than the reference force, then two reference springs can be connected in parallel. In this case, the measured force is equal to \(\vec( 2 F_0 ) \) . The forces \(\vec( 3 F_0 ) \) , \(\vec( 4 F_0 ) \), etc. can be measured similarly.

Comparison of force \(\vec(F ) \) with the standard. \(\vec(F) \) = \(\vec(2 F_0) \)

Measuring forces less than \(\vec(2 F_0)\)

Comparison of force \(\vec(F ) \) with the standard. \(\vec(F) \) = \(\vec(2 F_0) \cos (\alpha) \)

The reference force in the International System of Units is called Newton(N).

A force of 1 N imparts an acceleration of 1 m/s2 to a body weighing 1 kg.

Dimension [N]

\[ 1\text(N) = 1\dfrac(\text(kg)\cdot \text(m))(\text(s)^2)\]

In practice, there is no need to compare all measured forces with a standard. To measure forces, springs calibrated as described above are used. Such calibrated springs are called dynamometers . Strength is measured by the stretch of a dynamometer.