The movement of the body is called a directed segment of a straight line that connects the initial position of the body with its subsequent position. Displacement is a vector quantity.
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Basic concepts of kinematics
Kinematics called a section of mechanics in which the movement of bodies is considered without clarifying the reasons for this movement.
Mechanical movement bodies are called the change ᴇᴦο position in space relative to other bodies over time.
Mechanical movement relatively... The movement of the same body relative to different bodies is different. To describe the movement of a body, it is necessary to indicate in relation to which body the movement is considered. This body is called reference body.
The coordinate system associated with the reference body and the clock for counting time form frame of reference , which allows you to determine the position of a moving body at any time.
In the International System of Units (SI), the unit of length is meter, and per unit of time - second.
Every body has a certain size. Different parts of the body are in different places in space. However, in many problems of mechanics there is no need to indicate the positions of individual parts of the body. If the dimensions of the body are small in comparison with the distances to other bodies, then this body can be considered ᴇᴦο material point... This can be done, for example, when studying the motion of planets around the Sun.
If all parts of the body move in the same way, then such a movement is called progressive ... For example, the cabins in the attraction "Giant wheel", a car on a straight section of the path, etc. move progressively. During the translational movement of the body, ᴇᴦο can also be considered as a material point.
A body whose dimensions can be neglected under these conditions is called material point .
The concept of a material point plays an important role in mechanics.
Moving over time from one point to another, the body (material point) describes some line, which is called body trajectory .
The position of a material point in space at any time ( law of motion ) can be determined either by using the dependence of coordinates on time x = x(t), y = y(t), z = z(t) (coordinate method), or using the time dependence of the radius vector (vector method), drawn from the origin of coordinates to a given point (Fig. 1.1.1).
The movement of a body is called a directed segment of a straight line connecting the initial position of the body with ᴇᴦο the subsequent position. Displacement is a vector quantity.
The movement of the body is called a directed segment of a straight line that connects the initial position of the body with its subsequent position. Displacement is a vector quantity. - concept and types. Classification and features of the category "Displacement of a body is a directed line segment connecting the initial position of the body with its subsequent position. Displacement is a vector quantity." 2015, 2017-2018.
The projection is considered positive if (a x\u003e 0) from the projection of the beginning of the vector to the projection of its end you need to go in the direction of the axis. Otherwise, the projection of the vector (a x 0) from the projection of the beginning of the vector to the projection of its end must go in the direction of the axis. Otherwise, the projection of the vector (a x 0) from the projection of the beginning of the vector to the projection of its end must go in the direction of the axis. Otherwise, the projection of the vector (a x 0) from the projection of the beginning of the vector to the projection of its end must go in the direction of the axis. Otherwise, the projection of the vector (a x 0) from the projection of the beginning of the vector to the projection of its end must go in the direction of the axis. Otherwise, the projection of the vector (a x 
Do we pay for the way or travel when traveling by taxi? The ball fell from a height of 3 m, bounced off the floor and was caught at a height of 1 m. Find the path and movement of the ball. The cyclist moves in a circle with a radius of 30 m. What is the distance and movement of the cyclist in half a turn? For a full turn?
§ § 2.3 answer the questions at the end of the paragraph. Control. 3, page 15 In fig. shows the trajectory of the AVSD point movement from A to D. Find the coordinates of the points of the beginning and end of the movement, the path traveled, the movement, the projection of the movement on the coordinate axis. Solve the problem (optional): The boat passed 2 km to the northeast, and then to the north for another 1 km. Find the displacement (S) and its modulus (S) by the geometric construction.
Weight Is a property of the body that characterizes its inertia. Under the same influence from the surrounding bodies, one body can quickly change its speed, while the other under the same conditions - much more slowly. It is customary to say that the second of these two bodies is more inert, or, in other words, the second body has a greater mass.
If two bodies interact with each other, then as a result the speed of both bodies changes, that is, in the process of interaction, both bodies acquire accelerations. The ratio of the accelerations of the two given bodies turns out to be constant under any impacts. 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.
Power Is a quantitative measure of the interaction of bodies. Force is the cause of the change in body speed. In Newtonian mechanics, forces can have a different physical nature: friction force, gravity force, elastic force, etc. Force is vector quantity... The vector sum of all forces acting on the body is called resultant force.
To measure forces, you must set standard of strength and way of comparison other forces with this standard.
A spring stretched to a certain specified length can be taken as a standard of force. Power module F 0, with which this spring, at a fixed tension, acts on a body attached to its end, is called the standard of strength... The way to compare other forces with the standard is as follows: if the body under the action of the measured force and the reference force remains at rest (or moves uniformly and rectilinearly), then the forces are equal in modulus F = F 0 (fig. 1.7.3).
If the measured force F more (in modulus) than the reference force, then two reference springs can be connected in parallel (Fig. 1.7.4). In this case, the measured force is 2 F 0. The forces 3 can be measured similarly F 0 , 4F 0, etc.
Measurement of forces less than 2 F 0 can be performed according to the scheme shown in Fig. 1.7.5.
The reference force in the International System of Units is called newton (H).
A force of 1 N imparts an acceleration of 1 m / s 2 to a body weighing 1 kg
In practice, there is no need to compare all measured forces with a standard. For measuring the forces, springs are used that have been calibrated as described above. These calibrated springs are called dynamometers ... The force is measured by the tension of the dynamometer (Fig. 1.7.6).
Newton's laws of mechanics -three laws underlying the so-called. classical mechanics. Formulated by I. Newton (1687). The first law: "Every body continues to be held in its state of rest or uniform and rectilinear motion, until and since it is forced by the applied forces to change this state." The second law: "The change in the momentum is proportional to the applied driving force and occurs in the direction of the straight line along which this force acts." The third law: "Action is always equal and opposite opposition, otherwise, the interactions of two bodies against each other are equal and directed in opposite directions." 1.1. Law of Inertia (Newton's First Law)
: a free body, which is not acted upon by forces from other bodies, is in a state of rest or uniform rectilinear motion (the concept of velocity here is applied to the center of mass of a body in the case of non-translational motion). In other words, inertia is inherent in bodies (from the Latin inertia - “inactivity”, “inertia”), that is, the phenomenon of speed conservation, if external influences on them are compensated. Reference frames in which the law of inertia is fulfilled are called inertial reference frames (IFR). For the first time, the law of inertia was formulated by Galileo Galilei, who, after many experiments, concluded that no external reason is needed for a free body to move at a constant speed. Prior to this, a different point of view (dating back to Aristotle) \u200b\u200bwas generally accepted: a free body is at rest, and a constant force must be applied to move at a constant speed. Subsequently, Newton formulated the law of inertia as the first of his three famous laws. Galileo's principle of relativity: in all inertial reference frames, all physical processes proceed in the same way. In a frame of reference brought to a state of rest or uniform rectilinear motion relative to an inertial frame of reference (conventionally - “at rest”) all processes proceed in the same way as in a resting frame. It should be noted that the concept of an inertial reference system is an abstract model (an ideal object considered instead of a real object. Examples of an abstract model are an absolutely rigid body or a weightless thread), real reference frames are always associated with some object and the correspondence of the actually observed motion of bodies in such systems the calculation results will be incomplete. 1.2 Law of motion
- a mathematical formulation of how a body moves or how a more general movement occurs. In the classical mechanics of a material point, the law of motion represents three dependences of three spatial coordinates on time, or the dependence of one vector quantity (radius vector) on time, type. The law of motion can be found, depending on the problem, either from the differential laws of mechanics, or from the integral ones. Law of energy conservation
- the basic law of nature, which states that the energy of a closed system is conserved in time. In other words, energy cannot arise from nothing and cannot disappear into nowhere, it can only pass from one form to another. The law of conservation of energy is found in various branches of physics and manifests itself in the conservation of various types of energy. For example, in classical mechanics, the law manifests itself in the conservation of mechanical energy (the sum of potential and kinetic energies). In thermodynamics, the law of conservation of energy is called the first law of thermodynamics and speaks of the conservation of energy together with thermal energy. Since the law of conservation of energy does not refer to specific quantities and phenomena, but reflects a general, applicable everywhere and always, regularity, it is more correct to call it not a law, but the principle of conservation of energy. A special case - The law of conservation of mechanical energy - the mechanical energy of a conservative mechanical system is preserved in time. Simply put, in the absence of forces such as friction (dissipative forces), mechanical energy does not arise from nothing and cannot disappear anywhere. Ek1 + En1 \u003d Ek2 + En2 The law of conservation of energy is an integral law. This means that it consists of the action of differential laws and is a property of their combined action. For example, it is sometimes said that the impossibility of creating a perpetual motion machine is due to the law of conservation of energy. But this is not the case. In fact, in each project of a perpetual motion machine, one of the differential laws is triggered and it is he who makes the engine inoperative. The law of conservation of energy simply generalizes this fact. According to Noether's theorem, the law of conservation of mechanical energy is a consequence of the homogeneity of time. 1.3. The law of conservation of momentum (Law of conservation of the amount of motion, 2nd Newton's law)
states that the sum of the momenta of all bodies (or particles) of a closed system is a constant value. From Newton's laws it can be shown that when moving in empty space, the momentum is conserved in time, and in the presence of interaction, the rate of its change is determined by the sum of the applied forces. In classical mechanics, the momentum conservation law is usually derived as a consequence of Newton's laws. However, this conservation law is also true in cases where Newtonian mechanics is not applicable (relativistic physics, quantum mechanics). Like any of the conservation laws, the momentum conservation law describes one of the fundamental symmetries, the homogeneity of space Newton's third law
explains what happens to two interacting bodies. Take for example a closed system consisting of two bodies. The first body can act on the second with some force F12, and the second - on the first with the force F21. How are forces related? Newton's third law states: the force of action is equal in magnitude and opposite in direction to the force of reaction. Let us emphasize that these forces are applied to different bodies, and therefore are not compensated at all. The law itself: Bodies act on each other with forces directed along the same straight line, equal in magnitude and opposite in direction:. 
1.4. Forces of inertia
Newton's laws, strictly speaking, are valid only in inertial reference frames. If we honestly write the equation of motion of a body in a non-inertial frame of reference, then it will look different from Newton's second law. However, often, to simplify the consideration, some fictitious “force of inertia” is introduced, and then these equations of motion are rewritten in a form very similar to Newton's second law. Mathematically, everything is correct (correct) here, but from the point of view of physics, a new fictitious force cannot be considered as something real, as a result of some real interaction. Let us emphasize once again: “the force of inertia” is just a convenient parametrization of how the laws of motion differ in inertial and non-inertial frames of reference. 1.5. Viscosity law
Newton's law of viscosity (internal friction) is a mathematical expression that relates the stress of internal friction τ (viscosity) and the change in the velocity of the medium v \u200b\u200bin space (deformation rate) for fluid bodies (liquids and gases): where the value of η is called the coefficient of internal friction or dynamic coefficient of viscosity (the CGS unit is poise). The kinematic coefficient of viscosity is the value μ \u003d η / ρ (the CGS unit is Stokes, ρ is the density of the medium). Newton's law can be obtained analytically by means of physical kinetics, where viscosity is usually considered simultaneously with thermal conductivity and the corresponding Fourier law for thermal conductivity. In the kinetic theory of gases, the coefficient of internal friction is calculated by the formula 
Where< u > is the average speed of the thermal motion of molecules, λ is the average free path.
Definition 1
Body trajectory Is a line that has been described by a material point as it moves from one point to another over time.
There are several types of movements and trajectories of a rigid body:
- translational;
- rotational, that is, movement in a circle;
- flat, that is, moving along a plane;
- spherical, characterizing the movement on the surface of the sphere;
- free, in other words, arbitrary.
Picture 1 . Determination of a point using coordinates x \u003d x (t), y \u003d y (t), z \u003d z (t) and radius vector r → (t), r 0 → is the radius vector of the point at the initial moment of time
The position of a material point in space at any time can be specified using the law of motion, determined by the coordinate method, through the dependence of coordinates on time x \u003d x (t), y \u003d y (t), z \u003d z (t)or from the time of the radius vector r → \u003d r → (t), drawn from the origin to the given point. This is shown in Figure 1.
Definition 2S → \u003d ∆ r 12 → \u003d r 2 → - r 1 → is a directed line segment connecting the starting point with the end point of the body trajectory. The value of the traversed path l is equal to the length of the trajectory traversed by the body in a certain period of time t.
Figure 2. Distance traveled l and the displacement vector s → for curvilinear motion of the body, a and b are the starting and ending points of the path, adopted in physics
Definition 3
Figure 2 shows that when a body moves along a curved trajectory, the displacement vector module is always less than the distance traveled.
Path is a scalar. Counts as a number.
The sum of two successive displacements from point 1 to point 2 and from currents 2 to point 3 is the movement from point 1 to point 3, as shown in Figure 3.
Picture 3 ... The sum of two successive displacements ∆ r → 13 \u003d ∆ r → 12 + ∆ r → 23 \u003d r → 2 - r → 1 + r → 3 - r → 2 \u003d r → 3 - r → 1
When the radius vector of a material point at a certain moment of time t is r → (t), at the moment t + ∆ t is r → (t + ∆ t), then its displacement ∆ r → during time ∆ t is equal to ∆ r → \u003d r → (t + ∆ t) - r → (t).
The displacement ∆ r → is considered a function of time t: ∆ r → \u003d ∆ r → (t).
Example 1
According to the condition, a moving plane is given, shown in Figure 4. Determine the type of trajectory of point M.
Picture 4
Decision
It is necessary to consider the frame of reference I, called "Airplane" with the trajectory of the point M in the form of a circle.
Reference system II "Earth" will be set with the trajectory of the existing point M in a spiral.
Example 2
A material point is given that moves from A to B. The value of the radius of the circle is R \u003d 1 m. Find S, ∆ r →.
Decision
While moving from A to B, the point travels a path that is equal to half of the circle written by the formula:
Substitute numerical values \u200b\u200band get:
S \u003d 3.14 · 1 m \u003d 3.14 m.
The displacement ∆ r → in physics is a vector connecting the initial position of a material point with the final one, that is, A with B.
Substituting the numeric values, we calculate:
∆ r → \u003d 2 R \u003d 2 1 \u003d 2 m.
Answer: S \u003d 3, 14 m; ∆ r → \u003d 2 m.
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Mechanical movement. Relativity of motion. Elements of kinematics. material point. Galileo's transformations. The classical law of addition of speeds
Mechanics is a branch of physics that studies the laws of motion and interaction of bodies. Kinematics is a branch of mechanics that does not study the causes of motion of bodies.
Mechanical movement - a change in the position of a body in space relative to other bodies over time.
A material point is a body, the dimensions of which can be neglected under these conditions.
The motion is called translational, in which all points of the body move in the same way. A motion is called translational in which any straight line drawn through the body remains parallel to itself.
Kinematic characteristics of movement
Trajectory – line of movement. S - path – trajectory length.
S - displacement - a vector connecting the starting and ending position of the body.
Relativity of motion. Reference system - a set of reference bodies, coordinate systems and an instrument for measuring time (hours)
coordinate systemRectilinear uniform motion is called such a motion in which the body makes the same movements for any equal intervals of time. Velocity is a physical quantity equal to the ratio of the displacement vector to the time interval during which this displacement occurred. The speed of uniform rectilinear motion is numerically equal to the displacement per unit of time.
