What is kinematics? Definition and concept
The description of the movement of the body is a way to determine its position in space at any time. What is kinematics? It considers the movement of the body from the geometric side, not taking into account the reasons, that is, the forces that produce it.
For quite a long time all the kinematics was based on the works of the notorious Aristotle. The scientist argued that the speed of the fall of any body is directly proportional to its weight, and it cannot move in the absence of forces. The main task of kinematics is the mathematical determination of the characteristics of the motion of bodies and their position in time. For presentation, it does not require new beginnings and refers to the axioms of geometry.
The definition of what kinematics is is as follows: "This is a subsection of mechanics that studies the mechanical movement of a body, but does not consider the causes that cause it".
Idealization as a research method
So what is kinematics? This is the link that connects mechanics and geometry.The properties of physical bodies, liquid, solid and gaseous in mechanics, of which kinematics is a part, are idealized. A solid is considered by kinematics as an absolutely solid body. Those. the distance between its two particles cannot change. Drip liquid is regarded as absolutely incompressible, etc. Such a way to idealize subjects of study and there is a way of scientific research.
In nature, everything moves, and what we can observe is relative, but it can always be absolutized. The movement of the whole body is determined if we know the movement of each of its points. Therefore, before considering the movement of a body, the movement of points is considered. In nature, free fall is a natural, uniformly accelerated motion..
The trajectory of a body falling freely depends on the initial velocity vector. If it was thrown strictly vertically downwards, then it is a straight vertical segment, and its motion is uniformly variable.
Introducing the notion of a point facilitates research. The study of the relative movement of the body and is engaged in kinematics. The physics of circular motion, for example, says that a person’s speed,which goes along the edge of a rotating carousel, is equal to the vector sum of the speed of movement of the person himself and the speed of rotation of the carousel. This is the so-called velocity addition law.
Law of motion
The position of the so-called material point is determined by three coordinates. Its movement is a sequential and continuous passage through points of space, which occur over time and is accompanied by a change in coordinates. Its trajectory is the way in which it moves..
Kinematics of the motion of a material point
In addition to idealized bodies, this science introduced the concept of a material point as an object that has vanishingly small dimensions and infinitely small weight. The kinematics of a material point explores objects whose dimensions can be easily neglected.
Since first of all, compound motions are studied, that is, the stroke in two reference systems, mutually moving relative to each other, the kinematics of the point considers the coordinates of all points, the acceleration and the speed itself equal. And the coordinate system itself, which is associated with a point of reference, and the clock, which counts time, is a reference system that determines the position of a moving object at a time.
The kinematics of a point takes into account the distance traveled, speed, acceleration and displacement. Path - the length of the trajectory described by a point at a specified time interval. The displacement is a vector that connects the starting position of the point with the final one. The direction of speed will remain unchanged, and its value, with uneven movement, may change. Rectilinear motion is called equal-variable in the case when the velocity of an object changes in the same way in any time intervals.
In the case of an infinitely small mass, the point is the result of the separation of an object into an infinite number of infinitely small particles. In the case of a finite mass, a point is the result of unlimited compression of an object. Imagine a ball filled with matter, the radius of which is reduced to an infinitely small size, while the mass is preserved.
What are the speeds?
Absolute speed is that which is observed relative to fixed axes. Relative is the speed that a point has, if we consider moving axes, as stationary. And the portable is the speed that a point has, if we consider it fixed, and the axes - moving.
Motion is understood as continuous change of body position in time. The motion of a point is known, if it is possible for each arbitrary moment to indicate its position in space.
Analytical geometry provides various ways to determine the position of a point in space using special geometric quantities, called coordinates. This means that the motion of a point itself can be considered as a continuous change in its coordinates in time.
Direct and straight motion
The simplest of all movements is that in which the distance s of a point from the beginning along a straight line varies in proportion to time t. Denoting by s0 the distance of a point at the initial moment of time from the beginning of the distance, we obtain the equation of uniform motion in its general form:
s = s0 +/- vt,
where v is the proportionality coefficient. It is called the speed of uniform motion and has a physical meaning, as a measure of the change in the path with time.
The kinematics of the system owes its development to geological engineer Shal from France. The forward movement from him is a straight line taken in a body that moves parallel to itself.The forward movement should not be confused with straightforward. The body can move progressively and curvilinearly. Rectilinear motion is only a special case of translational. For example, the axis of the earth, which describes an ellipse, moves progressively.
Any movement that does not satisfy the condition of uniformity is called a variable. However, any variable movement in its infinitely small quantities can be considered as uniform. The speed of a variable movement is the speed of uniform, into which the movement in its elements splits.
There are a number of physical formulas of this science. They explain what kinematics is and make it possible to find out the path, speed, acceleration, body height, which was thrown vertically down or up, etc. For example, the equation of uniform rectilinear motion of a point, when the initial distance is zero, looks like this:
where s is the path, v is the speed, and t is the time.
Free falling body speed:
History of kinematics
Galileo Galilei conducted numerous experiments on the famous Leaning Tower of Pisa. He studied the free fall of objects and their inertia.His research just proved the fallacy of the ideas of Aristotle.
He stated the conclusions in his manuscript: "Conversation and mathematical proofs relating to two new branches of science relating to mechanics and the local movement."
Pierre Varignon's speech at a speech in front of the famous French Academy of Sciences, which he delivered in January 1700, is considered to be the birth of kinematics in the form in which we know it. At the same time, the concepts of speed and acceleration in a differential form were defined.
In the 18th century, Ampère first used the calculus of variations and laid the foundation for the independent development of kinematics.
After SRT was developed (the independent theory of relativity), which showed that space and time are not absolute values, but speed has a fundamental limitation, the kinematics received a new round of development within relativistic mechanics. She considers the laws of motion of particles and bodies at speeds that are comparable to the speed of light.
Thus, we figured out what kind of science is kinematics and what research methods it uses.