Kinematics of the material point: basic concepts, elements

The theme of our today's article will be the kinematics of the material point. What is this? What concepts are included in it and what definition is necessary to give this term? We will try to answer these and many other questions today.

Definition and concept

The kinematics of the material point is nothing more than a subsection of physics called "mechanics". She, in turn, studies the patterns of motion of certain bodies. The kinematics of a material point also deals with this task, but it does not do this in a general way. In fact, this subsection is studying methods that allow us to describe the motion of bodies. In this case, only the so-called idealized bodies are suitable for investigation. These include: a material point, an absolutely solid body and an ideal gas. Consider the concepts in more detail. We all know from the school bench that a material point is a body whose dimensions can be neglected in this or that situation. By the way, the kinematics of the translational motion of a material point first appears in the textbooks of the seventh class in physics. This is the simplest branch, therefore it is most convenient to begin acquaintance with science with its help. A separate issue is what are the elements of the kinematics of the material point. There are a lot of them, and conditionally they can be divided into several levels, having different complexity for understanding. If we talk, for example, about the radius vector, then, in principle, there is nothing extraordinarily complex in its definition. However, you will agree that it will be much easier for a student to understand it than for a student in a middle or high school. And to be honest, there is no need to explain the peculiarities of this term to high school students.

A Brief History of the Creation of Kinematics

Many, many years ago the great scientist Aristotle devoted the lion's share of his free time to the study and description of physics as a separate science. In particular, he worked on kinematics, trying to present its main theses and concepts, one way or another used in trying to solve practical and even ordinary tasks. Aristotle gave the initial idea of what are the elements of the kinematics of the material point. His works and works are very valuable for all mankind. Nevertheless, in his conclusions he made a considerable number of errors, and the blame for this was certain errors and miscalculations. The work of Aristotle was interested in another scientist - Galileo Galilei. One of the fundamental theses put forward by Aristotle, was that the movement of the body occurs only if some force acts on it, determined by intensity and direction. Galileo proved that this is a mistake. The force will affect the speed parameter, but not more. The Italian showed that force is the cause of acceleration, and it can arise only in mutuality with it. Galileo Galileo also paid considerable attention to the study of the process of free fall, deriving the corresponding patterns. Probably everyone remembers about his famous experiments, which he spent on the Leaning Tower of Pisa. In his works the basis of kinematic solutions was used by the physicist Ampere.

Initial concepts

As stated earlier, kinematics studies ways of describing the motion of idealized objects. In this case, in practice, the basics of mathematical analysis, ordinary algebra and geometry can be applied. But what are the concepts (concepts, not definitions and parametric values) that underlie this subsection of physics? First, everyone must clearly understand that the kinematics of the translational movement of the material point considers the movement without regard to force indicators. That is, to solve the corresponding problems we do not need formulas related to force. It does not take into account kinematics, no matter how many of them - one, two, three, at least several hundred thousand. Nevertheless, the existence of acceleration is still provided. In a number of problems, the kinematics of the motion of a material point dictates the determination of the magnitude of the acceleration. However, the causes of this phenomenon (that is, forces and their nature) are not considered, but are omitted.

Classification

We found out that kinematics investigates and applies methods of describing the motion of bodies without regard to the forces acting on them. Incidentally, another branch of mechanics deals with this problem, which is called dynamics. Newton's laws are already applied there , which allow one to determine in practice quite many parameters with a small number of known initial data. The basic concepts of the kinematics of a material point are space and time. And in connection with the development of science in general, and in this field, the question arose about the advisability of using such a combination.

From the very beginning, there was a classic kinematics. It can be said that it is not only the presence of both temporal and spatial gaps that is peculiar to it, but also their independence from the choice of this or that frame of reference. By the way, we'll talk about this a little later. Now just explain what is at stake. The space interval in this case will be considered a segment, the time interval is the interval of time. It seems that everything should be clear. So, these intervals will be considered absolute, invariant in classical kinematics, in other words not depending on the transition from one reference frame to another. Whether relativistic kinematics. In it, gaps in the transition between reference frames can vary. It would be more correct to say that they can not, but should, probably. Because of this, the simultaneity of two random events also becomes relative and is subject to special consideration. That is why in relativistic kinematics, two concepts - space and time - are combined into one.

Kinematics of the material point: velocity, acceleration and other quantities

To at least a little understand this subsection of physics, it is necessary to navigate in the most basic terms, to know the definitions and to represent what a particular quantity represents in general terms. Nothing is complicated in this, in fact, everything is very easy and simple. Let's consider, perhaps, for the beginning the basic concepts used in problems on kinematics.

Motion

By mechanical motion, we will consider a process in which an idealized object changes its position in space. At the same time, it can be said that the change is relative to other bodies. It is also necessary to take into account the fact that a certain time interval between two events occurs simultaneously. For example, you can select a certain interval, formed during the time elapsed between how the body came from one position to another. Let us also note that bodies can and will interact with each other according to the general laws of mechanics. This is exactly what the kinematics of the material point most often operates. The frame of reference is the following concept, which is inextricably linked with it.

Coordinates

They can be called ordinary data, which allows you to determine the position of the body at one time or another. Coordinates are inextricably linked with the notion of a reference frame, as well as a grid. Most often a combination of letters and numbers.

Radius vector

From the name it should already be clear what it is. Nevertheless, we will discuss this in more detail. If a point moves along a certain trajectory, and we know exactly the origin of one or another reference frame, then we can draw a radius vector at any time. It will connect the initial position of the point with the instantaneous or final point.

Trajectory

It will be called a continuous line, which is laid as a result of the motion of a material point in a particular frame of reference.

Speed (both linear and angular)

This is a value that can tell how quickly the body passes this or that distance interval.

Acceleration (both angular and linear)

Shows, by what law and how fast the speed parameter of the body is changing.

Perhaps, here they are - the main elements of the kinematics of the material point. It should be noted that both speed and acceleration are vector quantities. And this means that they do not just have some indicative value, but also a certain direction. By the way, they can be directed both in one direction, and in the opposite. In the first case, the body will accelerate, in the second - to brake.

The simplest tasks

The kinematics of the material point (velocity, acceleration and distance in which are practically fundamental concepts) does not even amount to a huge number of problems, but many of their various categories. Let's try to solve a fairly simple problem to determine the distance traveled by the body.

Suppose the conditions that we have on hand are as follows. The car of the rider stands on the starting line. The operator gives a signal with a flag, and the car abruptly breaks from its place. Determine if she will be able to set a new record in the race, if the distance equal to one hundred meters, the next leader passed in 7.8 seconds. Accelerate the car to take equal to 3 meters, divided by a second into a square.

So, how to solve this problem? It is quite interesting, because we do not require a "dry" definition of certain parameters. It is brightened by turns and a certain situation, which diversifies the process of solving and searching for indicators. But what should we be guided before we approach the task?

1. The kinematics of a material point implies the use of acceleration in this case.

2. A solution is proposed using the distance formula, since its numerical value appears in the conditions.

The task is generally simple. To do this, we take the distance formula: S = VoT + (-) AT ^ 2/2. What is the meaning? We need to find out how long the rider will go through the designated distance, and then compare the score with the record to see if he will beat him or not. To this end, we select the time, we obtain a formula for it: AT ^ 2 + 2VoT - 2S. This is nothing but a quadratic equation. But the car breaks off, so the initial speed will be 0. When solving the equation, the discriminant will be equal to 2400. To find the time, you need to extract the root. Let's make up to the second decimal place: 48,98. Let's find the root of the equation: 48.98 / 6 = 8.16 seconds. It turns out that the rider can not beat the existing record.