From everyday experience we can confirm the following conclusion: the speed and direction of movement of the body can be changed only during its interaction with another body.This gives rise to the phenomenon of inertia, which we discuss in this article.
What is inertia?Example of life observations
consider the case when some body at the initial stage of the experiment is already in motion.Later we will see that the reduction of speed and stop the body can not take place without permission, because the reason for that is the effect on him of another body.
You probably have more than once seen as the passengers who travel in truck suddenly lean forward during braking or pressed to the side at the turning point.Why is that?Explain further.When, for example, the athletes run a certain distance, they are trying to develop the maximum speed.Running through the finish line, you may not have to run, but you can not stop short, and therefore the athlete runs a few meters, that is, committing to coast.
From the above examples, we can conclude that all bodies have a feature to keep the speed and direction of movement, without being able at the same time instantly change them later action of a body.We can assume that in the absence of external action will keep the body and the speed and direction of movement as long as you want.So, what is inertia?This phenomenon save the velocity of the body in the absence of exposure to other bodies.
Opening inertia
This property of bodies discovered the Italian scientist Galileo Galilei.Based on their experiments and reasoning, he argued: if the body does not react with other bodies, it is either in a state of tranquility or moves uniformly.His discoveries have entered into a science as the law of inertia, but in more detail Rene Descartes formulated it, and even Sir Isaac Newton has introduced into its legal system.
Interesting fact: inertia, which has led us to the definition of Galileo, was considered in ancient Greece Aristotle, but because of the lack of development of science, the exact wording has not been given.Newton's first law states: there are
frame of reference with respect to which the body which moves forward, the speed remains constant if it does not operate any other body.The formula of inertia in the same general form and no, but below we present a set of other formulas, revealing its features.
Inertia bodies
We all know that the speed of a person, car, train, ship or other bodies increases gradually, when they start to move.All of you have seen the launch of missiles on TV or taking off of aircraft at the airport - they increase the speed is not jerky, but gradually.Observations and daily practice say that all bodies have a common feature: the speed of the motion of bodies in the process of their interaction is changing gradually, and therefore they need to change for a while.This feature is called the inertia of bodies.
All inert body, but not at all the same inertia.Of the two interacting bodies, it will be higher in the order, which will acquire a smaller acceleration.So, for example, when firing the gun becomes less acceleration than the cartridge.When the mutual repulsion of the adult and child adult skater receives less acceleration than the child.This indicates that the greater inertness adult.
To characterize the inertia of bodies have introduced special value - the mass of the body, it is usually denoted by m .In order to be able to compare the mass of different bodies, the mass of any of them should be considered a unit.Her choice may be arbitrary, but it must be convenient for practical use.The SI unit weight have a special reference made of a hard alloy of platinum and iridium.She wears a name we all know - kilogram.It should be noted that the inertia of the solid body there 2 types: the translational and rotational.In the first case is a measure of the inertia of the mass, in the second - the moment of inertia, which we will discuss later.
Inertia
So called scalar physical quantity.The SI unit of moment of inertia is kg * m2 .A generalized formula is:
There mi - a mass of points of the body, r i - the distance from the points of the body to the axis z in the spatial coordinate system.The verbal interpretation can say this: the moment of inertia is determined by the sum of products of elementary mass multiplied by the square of the distance from the base set.
There is another formula, characterized by a certain inertia:
There dm - mass element, r - the distance from the element dm to the axis z .Verbal can be formulated as follows: the moment of inertia of the system of material points, or relative to the pole body (point) - is the algebraic sum of the product of the masses of material points making up the body, the square of their distance to the pole 0.
It is worth mentioning that there are two kinds of moments of inertia - axialand centrifugal.There is also such a thing as the principal moments of inertia (GMI) (with respect to the principal axes).As a rule, they are always distinct.Now we can calculate the moments of inertia for many bodies (cylinder, disc, sphere, cone, sphere, and so on.), But will not go into clarifying all formulas.
reference systems
The first Newton's law dealt with the uniform rectilinear motion, which can be seen only in a certain frame of reference.Even approximate analysis of mechanical phenomena shows that the law of inertia is performed not in all frames of reference.
Consider a simple experiment: put the ball on a horizontal table in the car and watch his movements.If the train is in a state of mind with respect to the Earth, and the ball keeping calm as long as we do not act on it any other body (eg hand).Therefore, in the reference system that is associated with the Earth, the law of inertia is performed.
Imagine that the train will go relative to the Earth uniformly and straight.Then, in a reference system that is associated with the train, the ball will save the state of mind, and the one that is associated with the Earth - the state of uniform and rectilinear motion.Therefore, the law of inertia is performed not only in the frame of reference associated with the earth, but also in all other moving relative to the Earth uniformly and straight.
Now imagine that the train picks up speed quickly or abruptly turns (in all cases, it moves with acceleration relative to the earth).Then, as before, the ball maintains uniform and rectilinear motion, which he had before speeding train.However, with respect to the ball train itself emerges from a state of tranquility, though no bodies that have withdrawn it from him.This means that in the reference frame associated with the acceleration of the train relative to the earth, the law of inertia is broken.
Thus, the system of reference in which the law of inertia are called inertial.Those which are not performed - not inertial.Identify them simply: if the body moves uniformly in a straight line (in some cases - is calm), the inertial system;if uneven movement - non-inertial.
Inertia
It's a pretty notion of a multi-valued and therefore will try as much as possible to consider it in detail.Here is an example.You quietly stand in the bus.Suddenly he begins to move, and thus gaining acceleration.You will lean back past.But why?Who are you pulling?From the point of view of an observer on Earth (inertial reference system) you stay in place, while satisfying the first law of Newton.From the point of view of an observer in the bus, you start going backwards, as if by any force.In fact, your legs, which are connected by the friction with the floor of the bus, go ahead with it, and you,
losing his balance, had to fall back.Thus, to describe the motion of the body in a non-inertial frame of reference, and take into account the need to introduce additional forces that act on the part of the body ties with such a system.This force is the force of inertia.
should be noted that they were fictitious, because there is no single body or field under the influence of which you began to move the bus.Newton's laws to the forces of inertia do not apply, however, to use them along with the "real" forces allows to describe the motion in non-inertial reference systems of arbitrary using different tools.This is the whole point of the input forces of inertia.
So now you know what inertia, moment of inertia and inertial systems, inertial forces.We move on.
translational motion systems
Suppose that some body in a non-inertial reference frame moving with the acceleration a0 an inertial force acts F. For a non-inertial equation analogue Newton's second law has the form:
Where a0 - is acceleration of a body with mass m , which is caused by the force F with respect to a non-inertial frame of reference;Fіn - the force of inertia.The force F on the right side is the "real" in the sense that it is the resulting interaction of bodies, depending only on the difference of the coordinates and velocities of interacting material points that do not change from one frame to another, moving steadily.Therefore, it does not change and the force F. It is invariant with respect to the transition.But Fіn arises not because of the interaction of bodies, but because of the rapid movement of the reference frame, which is why it is changing at an accelerated transition to a different system, so it is not invariant.
centrifugal force of inertia
consider the behavior of bodies in a non-inertial frame of reference.XOY rotates relative to the inertial system, means we assume the Earth at a constant angular velocity ω.An example is the system in the figure below.
above shows the drive where the radially mounted rod and wearing a blue bead, "bound" to the axis of the disc elastic rope.While the drive is not spinning, the rope is not deformed.However, the unwinding drive the ball a little stretch a rope up until the elastic force favg not be such that is equal to the weight of the ball m its normal acceleration Apt = -ω2R, ie favg = -mω2R , wherein R - is the radius of the circle which describes during rotation of the ball around the system.
If the angular velocity ω disk remains constant, then the ball will stop movement relative to the axis OX.In this case, relative to the frame XOY, which is associated with the disk, the ball will be in a state of calm.This is explained by the fact that in this system, in addition to force favg, ball to the force of inertia Fcf , which is directed along the radius from the axis of rotation of the disk.Silanes having form as in the formula shown below, called the centrifugal force of inertia.It can only occur in the rotating frame.
Coriolis force turns out that when bodies move relatively rotating reference frames on them, in addition to the centrifugal force of inertia acts another force - the Coriolis.It is always perpendicular to the velocity vector of the body V, which means that it does not perform any work on the body.We emphasize that the Coriolis force manifests itself only when the body is moving with respect to a non-inertial reference system, which carries out the rotation.Its formula is as follows:
Since the expression (v * ω) is a vector product of vectors in parentheses, it can be concluded that the direction of the Coriolis force is determined by the rule of thumb in relation to them. Its unit is:
There Ө - is the angle between the vectors v and ω .
In conclusion
inertia - it's an amazing phenomenon that every day each person pursues a hundred times, even though we do not notice it.We think that the article has given you the answers to important questions about what the inertia of what strength and moments of inertia, who discovered the phenomenon of inertia. sure you were wondering.
