Application of the laws of kinematics in practice presentation. Kinematics basic concepts presentation prepared by the teacher of state educational institution. B) Mechanical movement is a physical quantity

Brief historical background Ø Ø Ø The development of kinematics as a science began in the ancient world and is associated with such a name as Galileo, who introduces the concept of acceleration. The development of kinematics in the 18th century. connected with the work of Euler, who laid the foundations of rigid body kinematics and created analytical methods for solving problems in mechanics. Deeper studies of the geometric properties of body movement were caused by the development of technology at the beginning of the 19th century. and, in particular, the rapid development of mechanical engineering. Large-scale research in the field of kinematics of mechanisms and machines belongs to Russian scientists: the founder of the Russian school of the theory of machines and mechanisms P.L. Chebyshev (1821-1894), L.V. Assur (1878-1920), N.I. Mertsalov (1866 - 1948), L.P. Kotelnikov (1865 -1944) and other scientists.

The basic concepts of kinematics: Kinematics (from the Greek. Κινειν - to move) - a section of mechanics in which the movement of bodies is considered without clarifying the reasons for this movement. The main task of kinematics: knowing the law of motion of a given body, determine all the kinematic quantities that characterize both the movement of the body as a whole and the movement of each of its points separately.

Kinematics is a description of the motion of bodies with mathematical answers to the questions: 1. Where? 2. When? 3. How? To get answers to the questions posed, the following concepts are needed:

The mechanical movement of a body (point) is the change in its position in space relative to other bodies over time.

Material point A body can be considered a material point if: 1. the distances covered by the body are much larger than the dimensions of this body; 2. the body moves translationally, that is, all its points move in the same way at any time.

Material point - a body, the size and shape of which can be neglected under the conditions of the problem under consideration; Trajectory - a conditional line of movement of a body in space; Path - the length of the trajectory; Move - Directional Line

Methods for specifying the movement of a point Ø natural With this method, the following are set: the trajectory of a point and the law of motion along this trajectory Ø is coordinate The position of a point relative to a certain reference system is given by its coordinates Equations of motion of a point in rectangular coordinates x = f 1 (t), y = f 2 (t ), z = f 3 (t)

Velocity: a vector value characterizes the speed of movement, shows what kind of movement the body makes per unit of time. Movement in which the body makes the same movements for any equal time intervals. called STRAIGHT UNIFORM. speed of uniform movement - [m / s] A movement in which the body makes uneven movements at equal intervals is called uneven speed of uneven movement: The direction of speed for: Ø rectilinear movement - invariably Ø curvilinear movement - tangential to the trajectory at a given point or variables.

Acceleration is a value that characterizes the change in speed with an uneven movement of the body. The average acceleration of uneven motion in the interval from t to t + ∆t is a vector quantity equal to the ratio of the change in velocity ∆v to the time interval ∆t: In free fall near the Earth's surface, where

The component aτ of the acceleration vector directed along the tangent to the trajectory at a given point is called tangential (tangential) acceleration. Tangential acceleration characterizes the modulus change of the velocity vector. The vector аτ is directed towards the movement of the point with an increase in its speed (figure - a) and in the opposite direction - with a decrease in speed (figure - b). a b

The tangential component of acceleration at is equal to the first time derivative of the modulus of speed, thereby determining the rate of change in speed modulus: The second component of acceleration, equal to: is called the normal component of acceleration and is directed along the normal to the trajectory to the center of its curvature (therefore, it is also called centripetal acceleration ). Full acceleration is the geometric sum of the tangential and normal components.

Description of the presentation for individual slides:

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Lesson topic: Basic concepts and equations of kinematics. The purpose of the lesson: to review the basic concepts of kinematics - trajectory, acceleration, speed, distance traveled and displacement.

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Outline What does mechanics study? Its main task. Kinematics. Basic concepts: reference body, coordinate system, reference system law of independence of motion material point and absolutely rigid body translational and rotational motion trajectory, path, displacement speed acceleration Classification of mechanical movements. Basic equations. Movement graphs.

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What does mechanics study? Its main task. The branch of physics - mechanics deals with the study of the mechanical motion of bodies. Mechanical movement is a change in the position of a body (in space) relative to other bodies over time. The main task of mechanics is to determine the position of the body at any given time.

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Kinematics. Basic concepts: Mechanics consists of two main sections: kinematics and dynamics. The section that does not consider the causes of mechanical motion and only describes its geometric properties is called kinematics. In kinematics, concepts such as trajectory, path and displacement, speed and acceleration are used.

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RELATIVITY OF MOTION. COUNTING SYSTEM. To describe the mechanical movement of a body (point), you need to know its coordinates at any time. To define coordinates, select a reference body and associate a coordinate system with it. Often the reference body is the Earth, with which a rectangular Cartesian coordinate system is associated. To determine the position of a point at any moment in time, it is also necessary to set the time origin. The coordinate system, the reference body with which it is connected, and the device for measuring time form a reference system with respect to which the movement of the body is considered

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The movement of real bodies is usually complex. Therefore, to simplify the consideration of movements, they use the law of independence of movements: any complex movement can be represented as the sum of independent simplest movements. The simplest movements include translational and rotational. In physics, models are widely used that make it possible to choose the main one that determines a given physical phenomenon from the whole variety of physical properties. One of the first models of real bodies is a material point and an absolutely rigid body. The law of independence of movements

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A body, the dimensions of which can be neglected under given conditions of motion, is called a material point. A body can be considered as a material point if its dimensions are small in comparison with the distance that it travels, or in comparison with the distances from it to other bodies. An absolutely rigid body is a body, the distance between any two points of which remains constant during its movement. These models make it possible to exclude deformation of bodies during movement. MATERIAL POINT AND ABSOLUTELY RIGID BODY.

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Translational and rotational movement. Translational is a movement in which a segment connecting any two points of a rigid body moves when moving parallel to itself. It follows from this that all points of the body during translational motion move in the same way, i.e. with the same speeds and accelerations. Rotational motion is called a movement in which all points of an absolutely rigid body move in circles, the centers of which lie on one straight line, called the axis of rotation, and these circles lie in planes perpendicular to the axis of rotation. Using the law of independence of movements, the complex movement of a rigid body can be considered as the sum of translational and rotational movements.

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Translational motion Select the correct statement about translational motion: Translational motion is the movement of a body in which a straight line segment connecting any two points belonging to this body moves while remaining parallel to itself. During translational motion, all points of a rigid body move in the same way, describe the same trajectories, and at each moment of time have the same speeds and accelerations. The downward movement of the skydiver is an example of forward movement. The moon moves progressively around the earth.

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TRAJECTORY, PATH, MOVEMENT The trajectory of movement is the line along which the body moves. The length of the trajectory is called the distance traveled. The path is a scalar physical quantity, the sum of the lengths of the trajectory segments, can only be positive. A move is a vector that connects the start and end points of the trajectory. EXAMPLES:  traversed path -  displacement vector - S a and b - start and end points of the path during curvilinear motion of the body. S Fig. 1 S Fig. 2 ACDENB - trajectory displacement vector - S

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EXAMPLE OF A DISPLACEMENT VECTOR Displacement is the difference between the final and initial position and is denoted by:

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Speed ​​The nature of a body's movement is determined by its speed. If the speed is constant, then the motion is called uniform and the equation of motion is as follows: [m / s2] The modulus of speed is: If the speed increases by the same amount over equal time intervals, then the motion is called uniformly accelerated. If the speed decreases by the same amount for equal periods of time, then the movement is called uniformly slowed down. These types of movements are called equal motion.

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AVERAGE AND INSTANT SPEEDS The rate of change in the position of a material point in space over time is characterized by average and instantaneous speeds. Average speed is a vector value equal to the ratio of displacement to the time interval during which this displacement occurred: Vav = s / t. The instantaneous speed is the limit of the ratio of displacement s to the time interval t during which this displacement took place, when t tends to zero: Vmin = limt -> 0 s / t.

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ADDITION OF VELOCITIES Consider the movement of a body in a moving coordinate system. Let S1 - displacement of a body in a moving coordinate system, S2 - displacement of a moving coordinate system relative to a stationary one, then S - displacement of a body in a stationary coordinate system is equal to: If the displacements of S1 and S2 are performed simultaneously, then: The frame of reference is equal to the sum of the speed of the body in the moving frame of reference and the speed of the moving frame of reference relative to the stationary one. This statement is called the classical law of addition of velocities.

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Acceleration The magnitude of the change in speed per unit of time is acceleration: In the course of movement, the speed can change, the absence of a change in speed leads to the absence of acceleration. An immovable body, or a body moving at a constant speed, has zero acceleration. Acceleration determines how much the speed increased during uniformly accelerated movement, and how much decreased during uniformly slowed movement in 1 second.

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For example: A cyclist moves with an acceleration a = 5m / s2, then every second his speed will take on the values:

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Average and instantaneous acceleration The quantity that characterizes the rate of change in speed is called acceleration. Average acceleration is a value equal to the ratio of the change in speed to the time interval during which this change occurred: asr = v / t. If v1 and v2 are instantaneous speeds at times t1 and t2, then v = v2-v1, t = t2-t1. Instant acceleration - the acceleration of the body at a given moment in time. This is a physical quantity equal to the limit of the ratio of the change in speed to the time interval during which this change occurred, when the time interval tends to zero: amgn = lim t -> 0 v / t.

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Basic equations.

Mechanics

Basic concepts of kinematics

Topic: Space, time, movement, speed. The main task of mechanics.

Mechanics (from the Greek. The art of building cars)

Section of physics about the movement of material objects and the interaction between them .

Mechanics

• Kinematics(traffic)

• Dynamics(force)

a section of mechanics in which the motion of bodies is considered without clarifying the reasons for this motion.

a section of mechanics that studies the causes of mechanical motion.

Basic concepts of kinematics

1. Space and time

The world around us is material

It exists objectively and realistically, i.e. Regardless of our consciousness and beyond.

Able to act on our senses and cause us certain sensations.

Space and time (time of speed of development of events)

Property of time: one-dimensionality, continuity

Time unit - second

The difference between the values ​​of any quantity is denoted by Δ (delta), for example: Δt - time interval.

The main spatial characteristic is the distance

Space properties:

- continuity

- three-dimensionality

-euclidean

Distance measure - meter

There are three levels of the structure of the world:

Megamir (world of galaxies)

MACROmir (from a grain of sand to the planets of the solar system)

MICROWORLD (molecules, atoms, elementary particles)

2. Reference system

Reference body - a body with respect to which the motion of other bodies is considered.

Frame of reference - a set of a coordinate system, a reference body with which it is associated, and an instrument for measuring time.

Coordinate systems

• One-dimensional - coordinate line

2D - coordinate plane

Spatial system

Coordinate (3D)

3. Mechanical movement (MD)

Mechanical movement body (point) is called the change in its position in space relative to other bodies over time.

4. Material point

Material point - a body, the size and shape of which can be neglected under the conditions of the problem under consideration. A body can be considered a material point if: 1.the distances covered by the body are much greater than the dimensions of this body; 2. the body is moving forward, i.e. all of its points move in the same way at any given time.

5. The main task of mechanics

Determination of the position of a particle in the selected frame of reference at any time

6. Trajectory, path of movement.

Trajectory - an imaginary line along which the body moves

Way ( S) Is the length of the trajectory. Moving Is a vector connecting the start and end points of the trajectory.

7. Speed

Speed is a physical vector quantity that characterizes the direction and speed of movement. Shows what movement the body has made per unit of time:

Instant speed- the speed of the body at a given moment in time or at a given point of the trajectory. It is equal to the ratio of small displacement to a small period of time during which this movement is completed:

average speed- a physical quantity equal to the ratio of the entire distance traveled to the entire time:

Solving problems

Problem 1... When is it possible, when it is impossible to take for a material point: scissors, a car, a rocket?

Objective 2. While walking, the young man walked 3 km north, where he met his girlfriend. After the meeting, they took a bus and drove 4 km eastward. Determine the path and travel taken by the young person

Problem 3. What value does the meter measure in a car: distance traveled or travel length?

Problem 4. When we say that the change of day and night on Earth is explained by the rotation of the Earth around its axis, we mean the frame of reference associated with ... a) planets; b) the sun; c) the Earth; d) any body.

1st level.

1) P about a given trajectory of movement of the body (see figure) find (graphically) its movement

2) Dictation "If you believe, you do not believe" (+ or -):

A) Mechanics - a part of physics that studies mechanical phenomena;

B) Mechanical movement is a physical quantity;

C) The movement of the ball along the chute is a mechanical phenomenon;

D) the center of the bicycle wheel (when driving on a horizontal road) makes a forward motion;

E) when falling from a certain height, the ball makes a translational motion.

Level 2:

A) the ruler can be taken as a material point if it makes a rotational movement on the table;

B) The trajectory of the end of the clock hand is a circle;

C) The Earth, when moving along its orbit, can be taken as a material point.

Level 3

3) The distance between points A and B in a straight line is 6 km. A person travels this distance back and forth in 2 hours. What is the path and movement of a person in 2 hours and 1 hour?

4) The cyclist moves in a circle with a radius of 100 mi makes 1 revolution in 2 minutes. Determine the path and movement of the cyclist in 1 min and 2 min.

"Motion of bodies" - Basic concepts of kinematics. And there is no such time interval for more than 5 minutes on the chart. Which of the bodies is moving with the fastest speed? Intensive preparation course for the Unified State Exam. - M .: Ayris-press, 2007. Relativity of motion. The traversed path l is the length of the trajectory traversed by the body in some time t.

"Uniform and uneven movement" - Features of this movement. Movement (distance traveled) Time Speed. Features of uneven movement. Uniform movement. The speed of the body with uniform movement can be determined by the formula. Yablonevka. The speed of the body with uneven movement can be determined by the formula. Irregular movement.

"The concept of kinematics" - Vector quantities. The value gives the number of revolutions per unit of time. Vector a. Angular velocity vector. Unit vector. A vector connecting the start point (1) of the movement to the end point (2). Vector addition of velocities. In textbooks, vectors are denoted in bold letters. Let's choose a rectangular coordinate system.

"Studying the movement of a body in a circle" - The movement of bodies in a circle. Run the test. The dynamics of the movement of bodies in a circle. Solve the problem. P.N. Nesterov. Decide for yourself. Checking the answers. A basic level of. Algorithm for solving problems. Body weight. Study of a method for solving problems.

"The movement of the body in a circle" - With what linear speed the wolf threw the hat. Period in case of uniform circular motion. The minute hand of the watch is 3 times longer than the second. Acceleration is directly proportional to the speed of movement. What is the minimum speed at which the aircraft should move. Angular movement. Angular velocity.

Point Kinematics - Coriolis acceleration. Euler's theorem. Rigid body kinematics. General case of compound body movement. Plane-parallel motion of a rigid body. Complex point movement. Angular velocity and angular acceleration. The causes of the Coriolis acceleration. Convert rotations. Complex motion of a rigid body.