Rectilinear movement. Presentation: Types of mechanical movements in production What is the name of body movement

Mechanical movement is a change in the position of a body in space relative to other bodies.

For example, a car is moving along the road. There are people in the car. People move along with the car along the road. That is, people move in space relative to the road. But relative to the car itself, people do not move. This shows up. Next we will briefly consider main types of mechanical movement.

Forward movement- this is the movement of a body in which all its points move equally.

For example, the same car makes forward motion along the road. More precisely, only the body of the car performs translational motion, while its wheels perform rotational motion.

Rotational movement is the movement of a body around a certain axis. With such a movement, all points of the body move in circles, the center of which is this axis.

The wheels we mentioned perform rotational motion around their axes, and at the same time, the wheels perform translational motion along with the car body. That is, the wheel makes a rotational movement relative to the axis, and a translational movement relative to the road.

Oscillatory motion- This is a periodic movement that occurs alternately in two opposite directions.

For example, a pendulum in a clock performs an oscillatory motion.

Translational and rotational movements are the simplest types of mechanical movement.

Relativity of mechanical motion

All bodies in the Universe move, so there are no bodies that are at absolute rest. For the same reason, it is possible to determine whether a body is moving or not only relative to some other body.

For example, a car is moving along the road. The road is located on planet Earth. The road is still. Therefore, it is possible to measure the speed of a car relative to a stationary road. But the road is stationary relative to the Earth. However, the Earth itself revolves around the Sun. Consequently, the road along with the car also revolves around the Sun. Consequently, the car makes not only translational motion, but also rotational motion (relative to the Sun). But relative to the Earth, the car makes only translational motion. This shows relativity of mechanical motion.

Relativity of mechanical motion– this is the dependence of the trajectory of the body, the distance traveled, movement and speed on the choice reference systems.

Material point

In many cases, the size of a body can be neglected, since the dimensions of this body are small compared to the distance that this body moves, or compared to the distance between this body and other bodies. To simplify calculations, such a body can conventionally be considered a material point that has the mass of this body.

Material point is a body whose dimensions can be neglected under given conditions.

The car we have mentioned many times can be taken as a material point relative to the Earth. But if a person moves inside this car, then it is no longer possible to neglect the size of the car.

As a rule, when solving problems in physics, we consider the movement of a body as motion of a material point, and operate with such concepts as the speed of a material point, the acceleration of a material point, the momentum of a material point, the inertia of a material point, etc.

Frame of reference

A material point moves relative to other bodies. The body in relation to which this mechanical movement is considered is called the body of reference. Reference body are chosen arbitrarily depending on the tasks to be solved.

Associated with the reference body coordinate system, which is the reference point (origin). The coordinate system has 1, 2 or 3 axes depending on the driving conditions. The position of a point on a line (1 axis), plane (2 axes) or in space (3 axes) is determined by one, two or three coordinates, respectively. To determine the position of the body in space at any moment in time, it is also necessary to set the beginning of the time count.

Frame of reference is a coordinate system, a reference body with which the coordinate system is associated, and a device for measuring time. The movement of the body is considered relative to the reference system. The same body relative to different reference bodies in different coordinate systems can have completely different coordinates.

Trajectory of movement also depends on the choice of reference system.

Types of reference systems can be different, for example, a fixed reference system, a moving reference system, an inertial reference system, a non-inertial reference system.

Characteristics of mechanical body movement:

- trajectory (the line along which the body moves),

- displacement (directed straight line segment connecting the initial position of the body M1 with its subsequent position M2),

- speed (ratio of movement to movement time - for uniform movement) .

Main types of mechanical movement

Depending on the trajectory, body movement is divided into:

Straight-line;

Curvilinear.

Depending on the speed, movements are divided into:

Uniform,

Uniformly accelerated

Equally slow

Depending on the method of movement, movements are:

Progressive

Rotational

Oscillatory

Complex movements (For example: a screw movement in which the body rotates uniformly around a certain axis and at the same time makes a uniform translational movement along this axis)

Forward movement - This is the movement of a body in which all its points move equally. In translational motion, any straight line connecting any two points of the body remains parallel to itself.

Rotational motion is the movement of a body around a certain axis. With such a movement, all points of the body move in circles, the center of which is this axis.

Oscillatory motion is a periodic motion that occurs alternately in two opposite directions.

For example, a pendulum in a clock performs an oscillatory motion.

Translational and rotational movements are the simplest types of mechanical movement.

Straight and uniform movement is called such a movement when, for any arbitrarily small equal intervals of time, the body makes identical movements . Let us write down the mathematical expression of this definition s = v? t. This means that the displacement is determined by the formula, and the coordinate - by the formula .

Uniformly accelerated motion is the movement of a body in which its speed increases equally over any equal intervals of time . To characterize this movement, you need to know the speed of the body at a given moment in time or at a given point in the trajectory, t . e . instantaneous speed and acceleration .

Instantaneous speed- this is the ratio of a sufficiently small movement on the section of the trajectory adjacent to this point to the small period of time during which this movement occurs .

υ = S/t. The SI unit is m/s.

Acceleration is a quantity equal to the ratio of the change in speed to the period of time during which this change occurred . α = ?υ/t(SI system m/s2) Otherwise, acceleration is the rate of change of speed or the increase in speed for each second α. t. Hence the formula for instantaneous speed: υ = υ 0 + α.t.

The displacement during this movement is determined by the formula: S = υ 0 t + α . t 2 /2.

Equally slow motion motion is called when the acceleration is negative and the speed uniformly slows down.

With uniform circular motion the angles of rotation of the radius for any equal periods of time will be the same . Therefore the angular speed ω = 2πn, or ω = πN/30 ≈ 0.1N, Where ω - angular speed n - number of revolutions per second, N - number of revolutions per minute. ω in the SI system it is measured in rad/s . (1/c)/ It represents the angular velocity at which each point of the body in one second travels a path equal to its distance from the axis of rotation. During this movement, the velocity module is constant, it is directed tangentially to the trajectory and constantly changes direction (see . rice . ), therefore centripetal acceleration occurs .

Rotation period T = 1/n - this time , during which the body makes one full revolution, therefore ω = 2π/T.

Linear speed during rotational motion is expressed by the formulas:

υ = ωr, υ = 2πrn, υ = 2πr/T, where r is the distance of the point from the axis of rotation. The linear speed of points lying on the circumference of a shaft or pulley is called the peripheral speed of the shaft or pulley (in SI m/s)

With uniform motion in a circle, the speed remains constant in magnitude but changes in direction all the time. Any change in speed is associated with acceleration. Acceleration that changes speed in direction is called normal or centripetal, this acceleration is perpendicular to the trajectory and directed to the center of its curvature (to the center of the circle, if the trajectory is a circle)

α p = υ 2 /R or α p = ω 2 R(because υ = ωR Where R circle radius , υ - point movement speed)

Relativity of mechanical motion- this is the dependence of the trajectory of the body, the distance traveled, movement and speed on the choice reference systems.

The position of a body (point) in space can be determined relative to some other body chosen as the reference body A . The reference body, the coordinate system associated with it, and the clock constitute the reference system . The characteristics of mechanical movement are relative, t . e . they can be different in different reference systems .

Example: the movement of a boat is monitored by two observers: one on the shore at point O, the other on the raft at point O1 (see . rice . ). Let us mentally draw through the point O the XOY coordinate system - this is a fixed reference system . We will connect another X"O"Y" system to the raft - this is a moving coordinate system . Relative to the X"O"Y" system (raft), the boat moves in time t and will move at speed υ = s boats relative to raft /t v = (s boats- s raft )/t. Relative to the XOY (shore) system, the boat will move during the same time s boats where s boatsmoving the raft relative to the shore . Speed ​​of the boat relative to the shore or . The speed of a body relative to a fixed coordinate system is equal to the geometric sum of the speed of the body relative to a moving system and the speed of this system relative to a fixed one .

Types of reference systems can be different, for example, a fixed reference system, a moving reference system, an inertial reference system, a non-inertial reference system.

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).

The 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.

We denote the period 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.

To find the coordinates of a moving body at any moment in time, you need to know the projections of the displacement vector on the coordinate axes, and therefore the displacement vector itself. What you need to know for this. The answer depends on what kind of movement the body makes.

Let's first consider the simplest type of movement - rectilinear uniform motion.

A movement in which a body makes equal movements at any equal intervals is called rectilinear uniform movement.

To find the displacement of a body in uniform rectilinear motion over a certain period of time t, you need to know what movement a body makes per unit of time, since for any other unit of time it makes the same movement.

The movement made per unit of time is called speed body movements and are designated by the letter υ . If movement in this area is denoted by , and the time period is denoted by t, then the speed can be expressed as a ratio to . Since displacement is a vector quantity, and time is a scalar quantity, then speed is also a vector quantity. The velocity vector is directed in the same way as the displacement vector.

Speed ​​of uniform linear motion of a body is a quantity equal to the ratio of the movement of the body to the period of time during which this movement occurred:

Thus, speed shows how much movement a body makes per unit time. Therefore, to find the displacement of a body, you need to know its speed. The movement of the body is calculated by the formula:

The displacement vector is directed in the same way as the velocity vector, time t- scalar quantity.

Calculations cannot be carried out using formulas written in vector form, since a vector quantity has not only a numerical value, but also a direction. When making calculations, they use formulas that include not vectors, but their projections on the coordinate axes, since algebraic operations can be performed on projections.

Since the vectors are equal, their projections onto the axis are also equal X, from here:

Now you can get a formula for calculating the coordinates x points at any given time. We know that

From this formula it is clear that with rectilinear uniform motion, the coordinate of the body linearly depends on time, which means that with its help it is possible to describe rectilinear uniform motion.

In addition, it follows from the formula that to find the position of the body at any time during rectilinear uniform motion, you need to know the initial coordinate of the body x 0 and the projection of the velocity vector onto the axis along which the body moves.

It must be remembered that in this formula v x- projection of the velocity vector, therefore, like any projection of a vector, it can be positive and negative.

Rectilinear uniform motion is rare. More often you have to deal with movement in which the movements of the body can be different over equal periods of time. This means that the speed of the body changes somehow over time. Cars, trains, airplanes, etc., a body thrown upward, and bodies falling to the Earth move at variable speeds.

With such a movement, you cannot use a formula to calculate the displacement, since the speed changes over time and we are no longer talking about a specific speed, the value of which can be substituted into the formula. In such cases, the so-called average speed is used, which is expressed by the formula:

average speed shows the displacement that a body makes on average per unit of time.

However, using the concept of average speed, the main problem of mechanics - determining the position of a body at any moment in time - cannot be solved.

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 the 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 motion.

see also

Links

• Mechanical movement (video lesson, 10th grade program)

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