Mechanical movement. Movement types Movement types and their description

Characteristics of mechanical body movement:

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

- displacement (a directed 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) .

The main types of mechanical movement

Depending on the trajectory, the movement of the body is divided into:

Straight-line;

Curvilinear.

Depending on the speed, the movements are divided into:

Uniform,

Equally accelerated

Equal slow

Depending on the method of movement, movements are:

Translational

Rotational

Oscillatory

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

Translational motion - this is the movement of the body, in which all its points move in the same way. In forward motion, any straight line connecting any two points of the body remains parallel to itself.

Rotational movement is the movement of a body around a certain axis. With such a movement, all points of the body move along 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 makes an oscillatory motion.

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

Straight and uniform movement such a movement is called when, for any arbitrarily small equal intervals of time, the body makes the same displacements . Let's write the mathematical expression of this definition s = υ? t. This means that the displacement is determined by the formula, and the coordinate is determined by the formula .

Equally accelerated movement the movement of a body is called, in which its speed for any equal time intervals increases in the same way . To characterize this movement, you need to know the speed of the body at a given moment in time or at a given point of the trajectory, i.e. . e . instantaneous speed as well as acceleration .

Instant speed is the ratio of a sufficiently small displacement on a trajectory segment adjacent to this point to a small time interval during which this displacement is performed .

υ = S / t. The SI unit is m / s.

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


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

Equal slow motion movement is called when the acceleration has a negative value, while the speed is uniformly decelerated.

With uniform movement around the circumference the angles of rotation of the radius for any equal time intervals will be the same . Therefore, the angular velocity ω = 2πn, or ω = πN / 30 ≈ 0.1N, where ω - angular speed n is the number of revolutions per second, N is the number of revolutions per minute. ω in the SI system is measured in rad / s . (1 / s) / 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 motion, the velocity module is constant, it is directed tangentially to the trajectory and constantly changes direction (see . rice . ), so there is a centripetal acceleration .

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

Linear speed during rotary 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 the shaft or pulley is called the peripheral speed of the shaft or pulley (in SI m / s)

With uniform movement around the circumference, the speed remains constant in magnitude, but changes in direction all the time. Any change in speed is associated with acceleration. Acceleration that changes the speed in a 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 movement is the dependence of the trajectory of the body movement, the distance traveled, movement and speed on the choice frame of reference.

The position of a body (point) in space can be determined with respect to any other body selected for the reference body A . The reference body, the associated coordinate system and the clock make up the reference system . The characteristics of mechanical movement are relative, t . e . they can be different in different frames of reference .

Example: two observers are watching the boat's movement: one on the shore at point O, the other on the raft at point O1 (see . rice . ). Let us mentally draw the coordinate system XOY through point O - this is a fixed frame of reference . Let's connect another system X "O" Y "with the raft - this is a moving coordinate system . With respect to the X "O" Y "(raft) system, the boat moves in time t and will move at a speed υ = s boats relative to the raft / t v = (s boats- s raft ) / t. In relation to the XOY (shore) system, the boat will move during the same time s boats where s boat movement relative to shore . Boat speed relative to shore or . The speed of a body relative to a stationary coordinate system is equal to the geometric sum of the speed of a body relative to a moving system and the speed of this system relative to a stationary one .

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

Curvilinear body movement

Curvilinear body movement definition:

Curvilinear motion is a type of mechanical motion in which the direction of speed changes. The speed module can vary.

Uniform body movement

Uniform body movement definition:

If a body travels equal distances in equal periods of time, then such a movement is called. With uniform motion, the modulus of speed is a constant value. Or it can change.

Uneven body movement

Uneven body movement definition:

If the body travels different distances at equal intervals of time, then such a movement is called uneven. With an uneven movement, the speed module is a variable value. The direction of speed can be changed.

Equivalent body movement

Equivalent body movement definition:

There is a constant value with equal motion. If in this case the direction of the velocity does not change, then we obtain a rectilinear, equally variable motion.

Uniformly accelerated body movement

Uniformly accelerated body movement definition:

Equal slow motion of the body

Equal slow motion body definition:

When we talk about the mechanical movement of a body, then we can consider the concept of translational movement of the body.

Details Category: Mechanics Published on 03/17/2014 18:55 Hits: 15751

Mechanical movement is considered for material point and for solid body.

Material point movement

Translational motion an absolutely rigid body is a mechanical movement, during which any segment of a straight line connected with this body is always parallel to itself at any moment in time.

If you mentally connect any two points of a rigid body with a straight line, then the resulting segment will always be parallel to itself in the process of translational movement.

When moving forward, all points of the body move in the same way. That is, they travel the same distance at the same time intervals and move in the same direction.

Examples of translational motion: movement of an elevator car, mechanical weighing cups, sledges rushing downhill, bicycle pedals, train platforms, engine pistons relative to cylinders.

Rotational motion

During rotational motion, all points of the physical body move in circles. All these circles lie in planes parallel to each other. And the centers of rotation of all points are located on one fixed straight line, which is called axis of rotation... The circles described by the points lie in parallel planes. And these planes are perpendicular to the axis of rotation.

Rotational motion is very common. Thus, the movement of points on the rim of a wheel is an example of a rotational movement. The rotational motion is described by a fan propeller, etc.

Rotational motion is characterized by the following physical quantities: angular velocity of rotation, period of rotation, frequency of rotation, linear velocity of a point.

Angular velocity a body with uniform rotation is called a value equal to the ratio of the angle of rotation to the time interval during which this rotation occurred.

The time it takes for the body to go through one complete revolution is called rotation period (T).

The number of revolutions that the body makes per unit of time is called speed (f).

The frequency of rotation and the period are related to each other by the ratio T = 1 / f.

If a point is at a distance R from the center of rotation, then its linear velocity is determined by the formula:

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

For example, a car is driving on a 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 people do not move relative to the car itself. This is manifested. Next, we will briefly consider main types of mechanical movement.

Translational motion- this is the movement of the body, in which all its points move in the same way.

For example, the same car is moving forward along the road. More precisely, only the car body performs translational motion, while its wheels rotate.

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

The wheels mentioned by us make a rotational movement around their axes, and at the same time the wheels make a translational movement together with the car body. That is, the wheel makes a rotational movement relative to the axis, and 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 makes an oscillatory motion.

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

Relativity of mechanical movement

All bodies in the Universe move, therefore there are no bodies that are in 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 driving on a road. The road is on planet Earth. The road is motionless. Therefore, it is possible to measure the speed of a vehicle relative to a stationary road. But the road is motionless 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 performs not only translational motion, but also rotational (relative to the Sun). But relative to the Earth, the car makes only translational motion. This is manifested relativity of mechanical movement.

Relativity of mechanical movement Is the dependence of the trajectory of the body movement, the distance traveled, movement and speed on the choice frame of reference.

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 resembles, or compared to the distance between this body and other bodies. To simplify calculations, such a body can be conventionally considered a material point with the mass of this body.

Material point Is a body whose dimensions can be neglected under these conditions.

The car we have mentioned many times can be mistaken for 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, the movement of a body is considered as material point movement, and operate with such concepts as the speed of a material point, acceleration of a material point, momentum of a material point, inertia of a material point, etc.

Frame of reference

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

The reference body is associated with coordinate system, which is the origin (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), a plane (2 axes) or in space (3 axes) is determined, respectively, by one, two or three coordinates. To determine the position of a body in space at any moment in time, it is also necessary to set the origin of time.

Frame of reference Is a coordinate system, a reference body with which the coordinate system is associated, and an instrument for measuring time. The movement of the body is also considered with respect to the frame of reference. The same body with respect to different reference bodies in different coordinate systems can have completely different coordinates.

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

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

Types of mechanical movement

Mechanical movement can be considered for different mechanical objects:

  • Material point movement is completely determined by the change in its coordinates in time (for example, two on a plane). The study of this is the kinematics of the point. In particular, the important characteristics of motion are the trajectory of a material point, displacement, speed and acceleration.
    • Rectilinear point movement (when it is always on a straight line, the speed is parallel to this straight line)
    • Curvilinear motion- 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 along a circle).
  • Solid body movement consists of the movement of any of its points (for example, the center of mass) and rotational movement around this point. It is studied by the kinematics of a rigid body.
    • 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 straightforward.
    • For description rotary motion- body movements relative to a selected point, for example, fixed at a point, - use the Euler angles. Their number in the case of three-dimensional space is three.
    • Also, for a solid body, there is flat motion- 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 - by the position of any two points.
  • Continuum motion... It is assumed here that the motion of individual particles of the medium is quite independent of each other (usually limited only by the conditions of continuity of the velocity fields), therefore, the number of defining coordinates is infinite (functions become unknown).

Motion geometry

Motion relativity

Relativity - the dependence of the mechanical movement of the body on the frame of reference. Without specifying a frame of reference, it makes no sense to talk about movement.

see also

Links

  • Mechanical movement (video lesson, grade 10 program)

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