Mechanical movement
Definition 1
A change in the location of a body (or its parts) relative to other bodies is called mechanical motion.
Example 1
For example, a person moving on an escalator in the subway is at rest relative to the escalator itself and moves relative to the walls of the tunnel; Mount Elbrus is at rest, conventionally the Earth, and moves with the Earth relative to the Sun.
We see that we need to indicate the point relative to which the movement is being considered; this is called the reference body. The reference point and the coordinate system to which it is connected, as well as the chosen method of measuring time, constitute the concept of reference.
The movement of a body, where all its points move equally, is called translational. To find the speed $V$ with which a body moves, you need to divide the path $S$ by the time $T$.
$ \frac(S)(T) = (V)$
The movement of a body around a certain axis is rotational. With this move, all points of the body move across the terrain, the center of which is considered to be this axis. And although the wheels make a rotational movement around their axes, at the same time, translational movement occurs along with the car body. This means that the wheel performs a rotational motion relative to the axis, and a translational motion relative to the road.
Definition 2
Oscillatory motion is a periodic movement that a body performs in turn in two opposite directions. The simplest example is a pendulum in a clock.
Translational and rotational are the simplest types of mechanical movement.
If point $X$ changes its location relative to point $Y$, then $Y$ changes its position relative to $X$. In other words, bodies move relative to each other. Mechanical motion is considered relative - to describe it you need to indicate relative to what point it is considered
Simple types of movement of a material body are uniform and rectilinear movements. It is uniform if the magnitude of the velocity vector does not change (the direction can change).
Movement is called rectilinear if the course of the velocity vector is constant (and the magnitude can change). A trajectory is a straight line on which the velocity vector is located.
We see examples of mechanical movement in everyday life. These are cars passing by, planes flying, ships sailing. We form simple examples ourselves, passing near other people. Every second our planet passes in two planes: around the Sun and its axis. And these are also examples of mechanical movement.
Varieties of movement
Translational motion is the automatic movement of a rigid body, while any stage of a straight line, clearly associated with a moving point, remains synchronous with its original position.
An important characteristic of the movement of a body is its trajectory, which represents a spatial curve, which can be shown in the form of conjugate arcs of different radii, each emanating from its center. A different position for any point of the body, which can change over time.
An elevator car or a Ferris wheel car moves progressively. Translational motion takes place in 3-dimensional space, but its main distinguishing feature - maintaining the parallelism of any segment to itself - remains in force.
The period is denoted by the letter $T$. To find the rotation period, you need to divide the rotation time by the number of revolutions: $\frac(\delta t)(N) = (T)$
Rotational motion - a material point describes a circle. During the rotational process of a completely rigid body, all its points describe a circle, which are in parallel planes. The centers of these circles lie on the same straight line, perpendicular to the planes of the circles and are called the axis of rotation.
The axis of rotation can be located inside the body and behind it. The axis of rotation in the system can be movable or fixed. For example, in a reference frame connected to the Earth, the rotation axis of the generator rotor at the station is motionless.
Sometimes the axis of rotation receives a complex rotational movement - spherical, when the points of the body move along the spheres. A point moves around a fixed axis that does not pass through the center of the body or a rotating material point; such movement is called circular.
Characteristics of linear motion: displacement, speed, acceleration. They become their analogues during rotational motion: angular displacement, angular velocity, angular acceleration:
- the role of movement in the rotational process has an angle;
- the magnitude of the rotation angle per unit time is the angular velocity;
- the change in angular velocity over a period of time is angular acceleration.
Oscillatory motion
Movement in two opposite directions, oscillatory. Oscillations that occur in closed concepts are called independent or natural oscillations. Fluctuations that occur under the influence of external forces are called forced.
If we analyze the swaying according to the characteristics that change (amplitude, frequency, period, etc.), then they can be divided into damped, harmonic, increasing (as well as rectangular, complex, sawtooth).
During free oscillations in real systems, energy losses always occur. Energy is spent working to overcome the force of air resistance. The friction force reduces the amplitude of vibrations, and they stop after some time.
Forced rocking is undamped. Therefore, it is necessary to replenish energy losses for each hour of fluctuation. To do this, it is necessary to act on the body from time to time with varying force. Forced oscillations occur with a frequency equal to changes in the external force.
The amplitude of forced oscillations reaches its greatest value when this coefficient is the same as the frequency of the oscillatory system. This is called resonance.
For example, if you periodically pull the rope in time with its vibrations, we will see an increase in the amplitude of its swing.
Definition 3
A material point is a body whose size can be neglected under certain conditions.
The car we often remember can be taken as a material point relative to the Earth. But if people move inside this car, then the size of the car can no longer be neglected.
When you solve problems in physics, the movement of a body is regarded as the movement of a material point, and such concepts as the speed of a point, the acceleration of a material body, the inertia of a material point, etc. are used.
Frame of reference
A material point moves relative to the inertia of other bodies. The body, according to the relation to which this automatic movement is considered, is called the body of reference. The reference body is chosen freely depending on the assigned tasks.
The location system is associated with the reference body, which assumes a reference point (coordinate base). The location concept has 1, 2 or 3 axes due to the condition of movement. The state of a point on a line (1 axis), plane (2 axes) or in a place (3 axes) is established in accordance with this by one, 2 or 3 coordinates.
In order to establish the position of the body in the spatial domain at any time period, it is necessary to set the start of the time count. A device for measuring time, a coordinate system, a reference point to which the coordinate system is connected - this is the reference system.
The movement of the body is considered in relation to this system. The same point, in comparison with different reference bodies in different coordinate concepts, has every chance of having completely different coordinates. The reference system also depends on the choice of motion trajectory
The types of reference systems can be varied, for example: a fixed reference system, a moving reference system, an inertial reference system, a non-inertial reference system.
The concept of motion is one of the philosophical categories, along with others, such as matter and time, that serve as the basis for the materialistic sciences. But we will not consider this issue so deeply now. Let's just see what they are and what types of motion there are from the point of view of classical mechanics.
In physics there is a special branch of mechanics - kinematics. She also studies its types, and considers the very movement of the object without its interaction with other bodies. The change in the position of a body relative to others in a given period of time is called mechanical movement, which in Greek sounds like “kinematics”.
Movement permeates our entire life. People and animals move, rivers and air, the Earth and the Sun move. It is quite possible that it was the initial observation of the processes of movement by the ancient Greeks that subsequently led to the creation of such a science as physics - at least to the creation of such sections as mechanics and kinematics.
The following types of mechanical are distinguished: translational and oscillatory. characterized by the fact that all points of the body move in the same direction at the same distance over the same time interval. During rotational motion or rotation, any points of an object move along circles whose centers are located on a line called the axis of rotation. An oscillatory movement is a movement that is periodically repeated completely or partially.
Considering the types of movement, we introduced two concepts - the movement of a point and a body. Strictly speaking, the description of the movement of a body as a whole is nothing more than a description of the movement of its various points. Therefore, it is often enough to characterize the movement of a point to understand the movement of the body itself. Translational motion is characterized by the same movement of all points of the body, so we can assume that by considering the movement of one point, we have determined how the body moves.
However, the types of movement are not limited to all of the above. The movement can be rectilinear or curved, uniform or uniformly accelerated. To describe the nature of the movement, it is necessary to again introduce a new concept - trajectory. It can be defined as the line along which a body moves. By running a pen over the paper, we see the mark that remains behind it. This is the trajectory of the pen.
Now, with the introduction of the concept of trajectory, we can take a closer look at the previously noted types of movement. So, with translation, different points may be different, but they remain parallel to themselves. An example is the body (but not the wheels) of a car moving straight. The movement of a needle in a sewing machine or a piston in a motor cylinder are other examples of translational motion.
The concept of trajectory provides an explanation for rectilinear and curvilinear motion. If the trajectory is a straight line, then it is, if not, then it is curved. An example of rotational curvilinear motion is Rotation will not be a translational motion.
Of course, all of the above is only part of what needs to be considered when touching on the topic “Types of movement”. To fully describe the nature of movement, it is necessary to introduce new concepts - such as speed, distance traveled, and reference system. Then it will be possible to understand in more detail the nature of the movement of both an individual point and the body as a whole. But even the material presented allows us to look a little into the many-sided world of movement.
The article examines the types of motion accepted in classical physics, gives examples of their different types and describes their distinctive features.
Mechanical movement of a body (point) is the change in its position in space relative to other bodies over time.
Types of movements:
A) Uniform rectilinear motion of a material point: Initial conditions 
. Initial conditions 
G) Harmonic oscillatory motion. An important case of mechanical motion is oscillations, in which the parameters of a point’s movement (coordinates, speed, acceleration) are repeated at certain intervals.
ABOUT scriptures of the movement . There are various ways to describe the movement of bodies. With the coordinate method specifying the position of a body in a Cartesian coordinate system, the movement of a material point is determined by three functions expressing the dependence of coordinates on time:
x= x(t), y=y(t) And z= z(t) .
This dependence of coordinates on time is called the law of motion (or equation of motion).
With the vector method the position of a point in space is determined at any time by the radius vector r= r(t) , drawn from the origin to a point.
There is another way to determine the position of a material point in space for a given trajectory of its movement: using a curvilinear coordinate l(t) .
All three methods of describing the motion of a material point are equivalent; the choice of any of them is determined by considerations of the simplicity of the resulting equations of motion and the clarity of the description.
Under reference system understand a reference body, which is conventionally considered motionless, a coordinate system associated with the reference body, and a clock, also associated with the reference body. In kinematics, the reference system is selected in accordance with the specific conditions of the problem of describing the motion of a body.
2. Trajectory of movement. Distance traveled. Kinematic law of motion.
The line along which a certain point of the body moves is called trajectorymovement this point.
The length of the trajectory section traversed by a point during its movement is called the path traveled .
The change in radius vector over time is called kinematic law
:
In this case, the coordinates of the points will be coordinates in time: x=
x(t),
y=
y(t) Andz=
z(t).
In curvilinear motion, the path is greater than the displacement modulus, since the length of the arc is always greater than the length of the chord contracting it
The vector drawn from the initial position of the moving point to its position at a given time (increment of the radius vector of the point over the considered period of time) is called moving. The resulting displacement is equal to the vector sum of successive displacements.
During rectilinear movement, the displacement vector coincides with the corresponding section of the trajectory, and the displacement module is equal to the distance traveled.
3. Speed. Average speed. Velocity projections.
Speed
- speed of change of coordinates. When a body (material point) moves, we are interested not only in its position in the chosen reference system, but also in the law of motion, i.e., the dependence of the radius vector on time. Let the moment in time 
corresponds to the radius vector 
a moving point, and a close moment in time 
- radius vector 
.
Then in a short period of time 
the point will make a small displacement equal to 
To characterize the movement of a body, the concept is introduced average speed
his movements: 
This quantity is a vector quantity, coinciding in direction with the vector 
. With unlimited reduction Δt the average speed tends to a limiting value called instantaneous speed 
:
Velocity projections.
A) Uniform linear motion of a material point: 
Initial conditions 
B) Uniformly accelerated linear motion of a material point: 
. Initial conditions 
B) Movement of a body along a circular arc with a constant absolute speed: 
Types of mechanical movement
Mechanical motion can be considered for different mechanical objects:
- Motion of a material point is completely determined by the change in its coordinates in time (for example, two on a plane). This is studied by the kinematics of a point. In particular, important characteristics of motion are the trajectory of a material point, displacement, speed and acceleration.
- Straightforward motion of a point (when it is always on a straight line, the speed is parallel to this straight line)
- Curvilinear movement- the movement of a point along a trajectory that is not a straight line, with arbitrary acceleration and arbitrary speed at any time (for example, movement in a circle).
- Rigid body motion consists of the movement of any of its points (for example, the center of mass) and rotational movement around this point. Studied by rigid body kinematics.
- If there is no rotation, then the movement is called progressive and is completely determined by the movement of the selected point. The movement is not necessarily linear.
- For description rotational movement- body movements relative to a selected point, for example, fixed at a point, use Euler Angles. Their number in the case of three-dimensional space is three.
- Also for a solid body there is flat movement- a movement in which the trajectories of all points lie in parallel planes, while it is completely determined by one of the sections of the body, and the section of the body is determined by the position of any two points.
- Continuum motion. Here it is assumed that the movement of individual particles of the medium is quite independent of each other (usually limited only by the conditions of continuity of velocity fields), therefore the number of defining coordinates is infinite (functions become unknown).
Geometry of movement
Relativity of motion
Relativity is the dependence of the mechanical motion of a body on the reference system. Without specifying the reference system, it makes no sense to talk about movement.
see also
Links
- Mechanical movement (video lesson, 10th grade program)
Wikimedia Foundation.
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See what “Mechanical movement” is in other dictionaries: mechanical movement - Change over time in the relative position in space of material bodies or the relative position of parts of a given body. Notes 1. Within mechanics, mechanical motion can be briefly called motion. 2. The concept of mechanical movement...
See what “Mechanical movement” is in other dictionaries: Technical Translator's Guide
See what “Mechanical movement” is in other dictionaries:- mechaninis judėjimas statusas T sritis fizika atitikmenys: engl. mechanical motion vok. mechanische Bewegung, f rus. mechanical movement, n pranc. mouvement mécanique, m … Fizikos terminų žodynas
See what “Mechanical movement” is in other dictionaries:- ▲ movement mechanical kinetics. kinetic. kinematics. mechanical processes processes of movement of material bodies. ↓ motionless, spreading, rolling... - Change over time in the relative position in space of material bodies or the relative position of parts of a given body...
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Demographic Encyclopedic Dictionary movement of organisms - ▲ mechanical movement form of movement: amoeboid (amoeba, blood leukocytes). ciliated (flagellates, spermatozoa). muscular. ↓ muscle tissue, movements (animal) ...
Ideographic Dictionary of the Russian Language movement - ▲ mechanical movement form of movement: amoeboid (amoeba, blood leukocytes). ciliated (flagellates, spermatozoa). muscular. ↓ muscle tissue, movements (animal) ...
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Contents 1 Physics 2 Philosophy 3 Biology ... Wikipedia In a broad sense, any change, in a narrow sense, a change in the position of a body in space. D. became a universal principle in the philosophy of Heraclitus (“everything flows”). The possibility of D. was denied by Parmenides and Zeno of Elea. Aristotle divided D. into... ...
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Books
- Fundamentals of demography. Textbook for universities, A. I. Shcherbakov, M. G. Mdinaradze, The theoretical foundations of demography, the relationship of economic reproduction of the population, methods of studying and analyzing demographic processes, the number and structure of the population,… Category: Demographics Series: Gaudeamus Publisher:
« Physics - 10th grade"
What quantities can describe the mechanical motion of a body?
There are several ways to describe, or what is the same thing, to specify the movement of a point. Let's look at two of them that are most often used.
Coordinate method.
We will specify the position of the point using coordinates. If a point moves, then its coordinates change over time. Since the coordinates of a point depend on time, we can say that they are functions of time.
Mathematically, this is usually written in the form
Equations (1.1) are called kinematic equations of motion of a point, written in coordinate form.
If the equations of motion are known, then for each moment in time we will be able to calculate the coordinates of the point, and therefore its position relative to the selected reference body. The form of equations for each specific movement will be quite specific.
The main task of kinematics is to determine the equation of motion of bodies.
The number of coordinates chosen to describe the motion depends on the conditions of the problem. If the point moves along a straight line, then one coordinate and, therefore, one equation is sufficient, for example, x(t). If the movement occurs on a plane, then it can be described by two equations - x(t) and y(t). Equations describe the movement of a point in space.
Vector method.
The position of a point can also be specified using a radius vector.
Radius vector- this is a directed segment drawn from the origin of coordinates to a given point.
When a material point moves, the radius vector that determines its position changes over time (rotates and changes length), i.e., is a function of time:
In the figure, the radius vector determines the position of the point at time t 1, and the radius vector 2 - at time t 2.
The above formula is equation of motion points written in vector form.
If it is known, then we can calculate the radius vector of a point for any moment in time, and therefore determine its position.
Specifying three scalar equations is equivalent to specifying one vector equation.
So, we know that the position of a point in space is determined by its coordinates or its radius vector.
The magnitude and direction of any vector are found by its projections on the coordinate axes. To understand how this is done, you first need to answer the question: what is meant by the projection of a vector onto an axis?
Let us depict the OX axis. Let us drop perpendiculars from the beginning A and end B of the vector onto the OX axis. Points A 1 and B 1 are projections of the beginning and end of the vector onto this axis, respectively.
Vector projection
The projection of a vector onto any axis is the length of the segment A 1 B 1 between the projections of the beginning and end of the vector onto this axis, taken with a “+” or “-” sign.
We will denote the projection of a vector with the same letter as the vector, but, firstly, without an arrow above it and, secondly, with an index below, indicating which axis the vector is projected onto. So, a x and a y are projections of the vector onto the coordinate axes OX and OY.
