What is inertia?
Inertia in physics is the ability of bodies to maintain a state of motion for a certain time in the absence of external forces. However, the concept of inertia is often used not only in physics, but also in our everyday life. This is what is usually called “inert”: a person who does not show any initiative at all, does only what others tell him, and does it extremely slowly, without any enthusiasm. “Moves by inertia,” we say when we want to emphasize that something is being done without any meaning, but simply because it was once done that way or because of a habit developed over the years. And if everything is more or less clear with the concept of inertia, thanks to such everyday examples, then the term “moment of inertia” requires a more detailed explanation, which we will do in our article.
Discovery of inertia
This property of bodies was discovered by the Italian scientist Galileo Galilei. Based on his experiments and reasoning, he argued: if a body does not interact with other bodies, then it either remains in a state of calm or moves rectilinearly and uniformly. His discoveries entered science as the Law of Inertia, but Rene Descartes formulated it in more detail, and Isaac Newton introduced it into his system of laws.
An interesting fact: inertia, the definition of which Galileo gave us, was considered in Ancient Greece by Aristotle, but due to the insufficient development of science, the exact formulation was not given. Newton's first law states: there are such reference systems relative to which a body that moves translationally maintains its speed constant unless other bodies act on it. There is no formula for inertia in a single and generalized form, but below we will give many other formulas that reveal its features.
2.1.1. Inertial and non-inertial reference systems.
The statement that inertial frames of reference exist is the essence of Newton's first law.
An inertial reference system
is a system relative to which a material point, free from external influences, is either at rest or moving uniformly and rectilinearly (i.e., a system in which Newton’s first law is satisfied).
A non-inertial frame of reference
is a system that moves relative to an inertial frame either translationally with acceleration or rotating.
It has been experimentally established that the heliocentric (stellar) reference system
, in which the origin of coordinates is at the center of the Sun, and the axes are drawn in the direction of certain stars.
Earth-related coordinate system
, strictly speaking non-inertial.
However, the effects due to its non-inertiality (the Earth rotates around its own axis and around the Sun) are negligible when solving many problems and conducting many experiments, and in many cases the system associated with the Earth
can be considered inertial.
Physics
Inertia
- the property of a body to, to a greater or lesser extent, prevent a change in its speed relative to the inertial frame of reference when exposed to external forces. It is mentioned in Russian-language literature, along with Inertia, as a synonym, but a slightly different definition is given. Inertia (from Latin inertia - inactivity, inertia, synonym: inertia.) - the property of bodies to remain in some reference systems in a state of rest or uniform rectilinear motion in the absence or with mutual compensation of external influences. The measure of inertia in translational motion is body mass. The measure of inertia in rotational motion is the moment of inertia.
Defragment the hard drive
Exam. Human
Defragmenting your hard drive is not really necessary in modern versions of Windows. The operating system, starting from Windows 7 and higher, will itself automatically defragment hard drives in the background. Solid state drives do not require traditional defragmentation at all. Although modern versions of Windows will optimize them, this process can no longer be called defragmentation.
But if you still want to defragment your hard drive, then I advise you to first analyze the disk, after which you can decide whether it is worth defragmenting the disk or not. The defragmentation process usually takes from several hours to two or more days, depending on its capacity.
I don’t recommend optimizing a solid-state drive, even if you really want to. You can find out why in the article Do I need to optimize the SSD or will Windows do it for you?
Disk defragmentation
Cookware not suitable for induction hob
If the kitchen utensil does not have magnetic properties, then it can be placed on the stove, but nothing will happen, it will not heat up.
Any cookware with a smooth bottom is suitable for an induction cooker.
Advice. When expanding your home range of cookware, you need to take into account that low pans with a wide bottom heat up faster.
List of unsuitable pots, saucepans and frying pans:
- all ceramic options;
- glass containers without a metal bottom;
- any dishes with a rough surface;
- everything that is less than 8 or 12 cm in diameter (depending on the type of slab).
- dishes with a thin bottom.
Reference systems
Newton's 1st law dealt with uniform linear motion, which can only be considered in a certain frame of reference. Even an approximate analysis of mechanical phenomena shows that the law of inertia is not satisfied in all reference systems.
Let's consider a simple experiment: put a ball on a horizontal table in a carriage and observe its movement. If the train is in a state of calm relative to the Earth, then the ball will remain calm until we act on it with another body (for example, a hand). Consequently, in the frame of reference that is associated with the Earth, the law of inertia is satisfied.
Let's imagine that the train will travel uniformly and rectilinearly relative to the Earth. Then, in the frame of reference that is connected with the train, the ball will maintain a state of calm, and in the one that is connected with the Earth, it will remain in a state of uniform and rectilinear motion. Consequently, the law of inertia is satisfied not only in the reference frame associated with the Earth, but also in all others moving uniformly and rectilinearly relative to the Earth.
Now imagine that the train quickly picks up speed or turns sharply (in all cases it moves with acceleration relative to the Earth). Then, as before, the ball retains the uniform and linear motion that it had before the train began to accelerate. However, relative to the train, the ball itself comes out of the state of calm, although there are no bodies that would take it out of it. This means that in the reference frame associated with the acceleration of the train relative to the Earth, the law of inertia is violated.
So, reference systems in which the law of inertia is satisfied are called inertial. And those in which it is not fulfilled are non-inertial. They are easy to define: if the body moves uniformly and in a straight line (in some cases this means calm), then the system is inertial; if the movement is uneven, it is non-inertial.
What is a strong person: the main signs of fortitude
I seriously thought about the question of what a strong person is. Previously, I was confident that I could handle anything, but now I increasingly come to the conclusion that I lack character, some skills and qualities that would help me endure stressful situations more calmly and confidently. The life of an adult is full of different events. Of course, I would like everything around to be joyful, filled with goodness and happiness, but unfortunately, it doesn’t happen that way. You have to overcome many unpleasant events, and this requires strength of spirit and will.
I began to study literature on this topic and identified several main signs by which one can distinguish a strong person from a weak one:
A strong person A weak person Knows how to forgive, so he moves through life easily, because his soul is free and easy. He cannot let go of the situation, so he lives with a load of grievances in his soul. But this is precisely why he destroys himself, does not allow positive thoughts and emotions to get out. Knows how to admit mistakes made, and therefore takes responsibility for correcting them. It is not difficult for him to ask for forgiveness for what he has done, draws conclusions and changes for the better. He cannot admit that he is wrong, so he begins to blame everyone for everything. Living with this conviction, such a person continues to destroy himself from within. A strong person is able to stay on his chosen path, even if something doesn’t go according to his plan. He will perceive any difficulty as an opportunity to discover new facets in himself. A weak person, regardless of any difficulty, will immediately fall into despair and begin to say that everything in life is bad, that he is unlucky, and simply does not deserve happiness. A strong person knows how to stand up for himself and defend his values. A weak person begins to capitulate, smile helpfully where he needs to show his true face, and remain silent where he needs to say. It is not difficult for a strong person to defend his personal boundaries. To do this, he just needs to firmly say the word “no”
It doesn’t matter who needs to be refused – a relative, a friend, a work colleague. It is not difficult for a strong person to defend his personal boundaries. To do this, he just needs to firmly say the word “no”
It doesn’t matter who needs to be refused – a relative, a friend, a work colleague. A strong person knows how to control his emotions. He will not give in to impulses of anger or happiness. Self-control and self-control in such a person are developed at the highest level. If something unbalances a weak person, he will immediately report it, showing strong emotions. A strong person will never be upset if someone, not him, wins, and will not rejoice at the defeats of other people. The most important thing for a strong person is to remain yourself, and not to compare yourself with someone or, in general, to look up to someone. Constantly focuses on someone, so he thinks that he is an unhappy person. He does not see any uniqueness or originality in himself. Takes on complex tasks with pleasure and enthusiasm. He understands that there is a high probability that he will make a mistake, but he is not afraid to do so because he perceives any failure as an opportunity for personal growth. Constantly refuses difficult tasks because he is afraid of making mistakes and not being able to cope. He doesn’t set himself the goal of pleasing everyone, because that’s impossible. If you defend your position, then someone will definitely not like it. He tries to please everyone, looks for approval in the eyes of other people, and only then begins to take some actions. A strong person constantly finds new opportunities to get closer to his goal faster. A weak person puts off everything for an indefinite period of time, waiting for the most opportune moment.
After I became acquainted with these signs, I realized that there was something to work on myself. After all, I want to be a strong person, a shining example for my children. I believe that anyone who wants to achieve something in their life, to become an individual, must develop willpower and spirit, because a weak person simply does not have enough potential.
Moment of inertia
An authoritative person is a person whose opinions and actions have a high influence on others
Inertia manifests itself not only for linear motion, but also during rotation of bodies. The engine has a special device - a flywheel (in the picture on the right, the flywheel is painted dark gray and has teeth). The inertia of its rotation helps the engine operate normally. The energy of the expanding gases when the fuel ignites pushes the piston down, and then it needs to go up, pushing out the combustion products. Without a flywheel, the piston would not be able to rotate the crankshaft without jerking. An engine without a flywheel will stall.
Well, many people are familiar with spinners and tops.
It’s just that in the examples given, the shape of the body does not change. Will the inertia of a body change when its shape changes?
Figure skating spin
Many people can remember figure skating. The figure skater’s body weight does not change during the performance. But its rotation speed instantly increases, as soon as you press your arms and legs, you stretch out. Those. As the radius of the body decreases, the rotation speed increases. Those. Should the inertia of the body decrease? Let's figure it out.
Let's return to the formulas. The speed of a rotating body is described as the product of angular speed (omega) and radius:
Speed of a rotating body
In this case, the kinetic energy of the rotating body will take the form:
The product of body mass and radius squared is highlighted in blue. This quantity is called the moment of inertia of a rotating body and is denoted by the Latin letter I (i).
A measure of the inertia of a rotating body is the moment of inertia, which depends on the mass of the body and the distance of this mass from the center of rotation.
Let's imagine that the girl not only rotates the weight above her, but also walks. Then the total kinetic energy of the girl with the load will take the form:
The first part describes the kinetic energy of a girl with a load moving rectilinearly at a certain speed, and the second describes the kinetic energy of a rotating load. Total kinetic energy is the sum of the energy of a rectilinearly moving body and the energy of a rotating body. In the same way, the kinetic energy will be calculated for a spinning top moving on a table or a cylinder sliding down an inclined plane.
Since a rotating body can have a shape different from a point or a small ball, the formula for the moment of inertia can take different forms for more accurate calculations.
Some formulas for calculating the moment of inertia for bodies of different shapes
Example.
Cylinders of the same mass (m1 = m2), but different radii (r1 < r2), roll down a hill of height h. Which cylinder will roll faster? Which body has less inertia?
Cylinders of the same mass, but different radii, roll down a hill of height h
At the top point, the kinetic energy of both cylinders will be zero, since the speed is zero. The potential energy will be the same and maximum.
Potential and kinetic energy of cylinders 1 and 2 at the top point
When the cylinders roll down, according to the law of conservation of energy, the potential energy turns into kinetic energy and at the lowest point it will be equal to zero, since the height is zero. And the kinetic energy at the bottom point will be the sum of the translational kinetic energy and the kinetic energy of the rotating body and will also be the same for both bodies, since their potential energies were equal.
Kinetic energy of the first and second cylinders at the lowest point
But since the radius of the first body is less than the second, then the moment of inertia of the first body is less than the second and it will be true:
Then the relation will be valid for the kinetic energy of translational motion:
Therefore, the speed of the first cylinder must be higher than the speed of the second, and it will roll faster. Since the measure of inertia of a rotating body is the moment of inertia, the first body with a smaller radius and a smaller moment of inertia will have less inertia than the second. It is easier for such a body to accelerate under the influence of any forces (gravity).
In conclusion
You can come to the logical conclusion of the topic. It turns out that inertia is not always a disease in psychology, but often it is simply one of the features of the nervous system. We are all different in our temperament, but we are not able to change this indicator.
Of course, in this case we are not talking about laziness. If you suffer from your own passivity, show apathy and do not want to make any efforts, you need to learn to work on yourself, on your complexes and fears, and get rid of indecision.
I would also like to note that for inert people, the emotional support of others is actually very important. Therefore, if you have such a person in your team or family, do not try to spread rot on him, try to encourage him at least from time to time, saying warm words.
And the following video will tell you even more information on the topic:
What to do if he is nearby?
So how do you understand that this is the kind of person in front of you? An inert person can be recognized by his behavior, by his actions. He is quite heavy to climb and in order to start doing any task he needs to tune in and swing. Such a person “flies in space”, he is apathetic to everything and does not worry about anything. An inert state makes him feel indifferent to what is happening around him. Life is easy for such people. Having experienced a stressful situation, they quickly forget about what is happening and do not torment themselves with memories, unlike active people.
If you entrust them with some work and explain everything step by step, then rest assured that they will cope with it perfectly. But under no circumstances should you put pressure on such people and rush them to answer. You will not achieve anything from them, but on the contrary, you will aggravate the situation. They must first of all figure it out themselves and, when they are ready, they will give you the expected result.
Relationships with such a person can be very difficult. If this is an inert man with whom you live together, but do not feel him close at all, then you should not suddenly take up his re-education. You need to think everything over carefully, weigh all the pros and cons, but also not forget about yourself. If you begin to present claims to your man that he is this and that, he will definitely present something to you and the situation will take on the character of a vicious circle of reproaches.
Therefore, I advise you to start with yourself. Remember if he was like this at the beginning of your relationship; perhaps his inertia became an attractive character trait for you at that moment. I know many girls who prefer calm partners. But when, after a while, you notice that his calmness and inaction are manifested in literally everything, this really becomes a problem.
Therefore, first you need to talk about a topic that worries you with your chosen one. There is no need to make harsh statements and statements addressed to him: he may simply not understand you. If you can’t really talk, the article “How to insist on talking” will come to the rescue. When you find out what is the reason for apathy, it will become much easier. And then it will be possible to make some joint decisions to eliminate the tension between you.
If a woman turns out to be inert in a relationship, then this is also fraught with problems. Yes, at the beginning of a relationship, it seems that things cannot be better, but after a while it’s no fun with such a person. A woman becomes boring, she has no opinion, she often reacts silently to certain circumstances, and agrees with everything. You will probably say that this is just every man’s dream! But believe me, it only seems so from the outside. People cannot live without emotions, experiences, worries. Of course, it’s better when they are pleasant, but in any case they should be present in a person’s life.
How to deal with inertia
Here again we need to separate recommendations for innately inert people and those who are simply lazy and inactive.
What should those who are not passive, but simply lazy, do?
- Indecisiveness is usually caused by low self-esteem. Then it turns out that to eliminate this illness, a constant increase in self-esteem will be required. Tell such a person that everything will work out for him, that he is great. Praise in every possible way even for minimal achievements.
- And if criticism is strongly required, then express it in such a way that a passive individual can look at the situation from a different angle, drawing the right conclusions from it. Oppression is strictly prohibited, because how such a person will perceive unreasoned criticism is unknown.
Recommendations for “going with the flow”
If you are naturally an inert personality type, then it won’t hurt to listen to the following advice:
- Choose a job so that you can feel like a real professional. When other people continually ask for help, you will feel confident and can improve your self-esteem.
- Are you missing even the slightest inspiration in life? Absolutely nothing can arouse interest in you, ignite at least some emotions? Then it is recommended to find a person who is simply burning with a certain idea, and join him in his efforts. And even if you are not captured by the same passion as him, you can learn the most valuable skills from him. For example, learn how to make plans and their subsequent implementation, as well as enjoy the process.
- Sometimes life challenges each of us. It requires making certain efforts, going somewhere, getting out of your “shell.” There is no need to try to “bury your head in the sand.” To begin with, try to soberly assess what is happening according to criteria from zero to ten points, as difficult as this will be for you. But at the same time, do not forget about the pleasure received from the implementation of your plans. Many inert people tend to deliberately exaggerate problems, downplaying the joy of victory.
- Introduce expressions with a strong positive connotation into your speech: “wonderful,” “great,” “I really like it.” Psychologists say that our thoughts and words create our entire life. Therefore, at first you will simply start saying positive statements, and then you yourself will not notice that life around you has become brighter, richer, more interesting.
We calculate the moment of inertia of an extended object
The moment of inertia is easily calculated for a very small (point) object if all points of the object are located at the same distance from the point of rotation. For example, in the previous example, if we assume that the golf ball is much smaller than the length of the string, then all its points are at the same distance from the point of rotation, equal to the radius of the circle of rotation \( r \). In this case, the moment of inertia has a familiar form:
where \(r\) is the distance at which the entire mass of the ball \(m\) is concentrated.
However, this ideal situation does not always occur. What is the moment of inertia of an extended object, for example a rod, rotating about one of its ends? After all, its mass is not concentrated at one point, but distributed along the entire length. Generally speaking, to determine the moment of inertia of an extended object, you need to sum up the moments of inertia of all material points of the object:
For example, the moment of inertia \( l \) of a system of two “point” golf balls with the same mass \( m \) at distances \( r_1 \) and \( r_2 \) is equal the sum of their individual moments of inertia \( l_1=mr_1^2 \) and \( l_2=mr_2^2 \):
How to determine the moment of inertia of a disk rotating about its center? You need to mentally divide the disk into many material points, calculate the moment of inertia of each such point and sum up the resulting moments of inertia. Physicists have learned to calculate the moments of inertia for many objects with a standard shape. Some of them are given in table. 11.1.
Let's try to calculate the moments of inertia of several objects with simple geometry.
Example: Slowing down a CD's rotation
CDs can spin at different angular speeds. This is necessary to ensure the same linear speed of reading information in areas located at different distances from the center of rotation. Let a disk with a mass of 30 g and a diameter of 12 cm first rotate at a speed of 700 revolutions per second, and after 50 minutes - at a speed of 200 revolutions per second. What is the average moment of force acting on the compact disc as the speed decreases in this way? The relationship between moment of force and angular acceleration has the form:
The moment of inertia of a disk with radius \( r \), rotating about its center in the plane of the disk, is expressed by the formula:
Substituting the values, we get:
Now we need to determine the angular acceleration, which is determined by the following formula:
The change in angular velocity \( \Delta\omega \) occurred over the period of time:
In this example, the change in angular velocity is:
where \( \omega_1 \) is the final, and \( \omega_0 \) is the initial angular velocity of the CD.
What are they equal to? An initial speed of 700 revolutions per second means that the disk travels \( 2\pi \) radians 700 times per second:
Likewise, a final speed of 200 revolutions per second means that the disk travels \(2\pi\) radians 200 times per second:
Substituting the values into the angular acceleration formula, we get:
Substituting the values of the moment of inertia and angular acceleration into the final formula for the moment of force, we obtain:
So, the average moment is 10-4 N·m, and what will be the force to create such a moment if it is applied to the edge of the disk? Its value can be easily calculated using the following formula:
It turns out that you don't need to apply that much force to slow down a CD this much.
Another example: lifting a load
The rotational motion sometimes does not look as obvious outwardly as the rotation of a compact disc. For example, lifting a load using a block is also an example of rotational motion. Although the rope and the load move translationally, the block itself rotates (Fig. 11.2). Let the radius of the block be 10 cm, its mass equal to 1 kg, the mass of the load equal to 16 kg, and a force of 200 N applied to the rope. Let's try to calculate the angular acceleration of the block.
In this example, you need to calculate the sum of all moments of forces \( \mathbf{\sum\! M} \) that act on the rope:
In this example, two moments of force act on the rope: one \( M_1 \) from the side of a load weighing \( mg \), and the other \( M_2 \) - from the side of the horizontal force \( F \):
From here we get the formula for angular acceleration:
These moments \( M_1 \) and \( M_2 \) have the same shoulder, equal to the block radius \( r \), therefore:
Since the block has the shape of a disk, then from the table. 11.1 we find its moment of inertia:
Substituting the expressions for \( l \), \( M_1 \) and \( M_2 \) into the formula for angular acceleration, we obtain:
Substituting the values, we get:
