translational movement - this is the mechanical movement of a system of points (absolutely rigid body), in which the straight line connecting any two points of this body, the shape and size of which do not change during the movement, remains parallel to its position at any previous moment in time.

The above illustration shows that, contrary to the widespread assertion, translational motion is not the opposite of rotational motion, but in the general case can be considered as a set of turns - rotations that have not ended. This implies that rectilinear motion is a rotation around a center of rotation infinitely distant from the body.

In the general case, translational motion occurs in three-dimensional space, but its main feature - the preservation of the parallelism of any segment to itself, remains in force.

Mathematically translational movement in its own way end result is equivalent to a parallel translation. However, considered as physical process it represents a variant of the helical motion in three-dimensional space (See Fig. 2)

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Translational and rotational movements.

Kinematics: Translational and rotational motion of a rigid body. Foxford Online Learning Center

Progressive movement. Material point

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Translational examples

Translationally moves, for example, an elevator car. Also, in the first approximation, the cabin of the Ferris wheel performs forward movement. However, strictly speaking, the movement of the Ferris wheel cabin cannot be considered progressive.

One of the most important characteristics of the movement of a point is its trajectory, in the general case, which is a spatial curve, which can be represented as conjugate arcs of various radii, each emanating from its center, the position of which can change in time. In the limit, the straight line can also be considered as an arc whose radius is equal to infinity.

In this case, it turns out that during translational motion in each this moment time, any point of the body makes a turn around its instantaneous center of rotation, and the length of the radius at the given moment is the same for all points of the body. The velocity vectors of the points of the body, as well as the accelerations they experience, are the same in magnitude and direction.

When solving problems theoretical mechanics it is convenient to consider the motion of a body as the addition of the motion of the center mass of the body and rotary motion the body itself around the center of mass (this circumstance is taken into account when formulating

Fig 1. Translational movement of the body on the plane from left to right, with an arbitrarily selected segment in it AB. First rectilinear, then curvilinear, turning into rotation of each point around its center with equal for a given moment, the angular velocities and equal turning radius values. points O- instantaneous turning centers to the right. R- their equal for each end of the segment, but different for different instants of time instantaneous turning radii.

translational movement- this is the mechanical movement of a system of points (absolutely rigid body), in which a straight line connecting any two points of this body, the shape and dimensions of which do not change during movement, remains parallel to its position at any previous moment in time.

The above illustration shows that, contrary to the widespread assertion, translational motion is not the opposite of rotational motion, but in the general case can be considered as a set of turns - rotations that have not ended. This implies that rectilinear motion is a turn around a center of turn infinitely distant from the body.

In the general case, translational motion occurs in three-dimensional space, but its main feature - the preservation of the parallelism of any segment to itself, remains in force.

Mathematically, translational motion is equivalent to parallel translation in its final result. However, considered as a physical process, it is a variant of helical motion in three-dimensional space (See Fig. 2)

Translational examples

Translationally moves, for example, an elevator car. Also, in the first approximation, the cabin of the ferris wheel makes translational motion. However, strictly speaking, the movement of the Ferris wheel cabin cannot be considered progressive.

One of the most important characteristics of the movement of a point is its trajectory, in the general case, which is a spatial curve, which can be represented as conjugate arcs of various radii, each emanating from its center, the position of which can change in time. In the limit, the straight line can also be considered as an arc whose radius is equal to infinity.

In this case, it turns out that during translational motion at each given moment of time, any point of the body makes a turn around its instantaneous center of rotation, and the length of the radius at the given moment is the same for all points of the body. The velocity vectors of the points of the body, as well as the accelerations they experience, are the same in magnitude and direction.

When solving problems of theoretical mechanics, it is convenient to consider the movement of a body as the addition of the movement of the center of mass of the body and the rotational movement of the body itself around the center of mass (this circumstance was taken into account when formulating Koenig's theorem).

Device examples

The principle of translational movement is implemented in the drawing instrument -

>>Physics: Movement of bodies. translational movement

A description of the motion of a body is considered complete only when it is known how each of its points moves.
We paid a lot of attention to the description of the movement of the point. It is for a point that the concepts of coordinates, velocity, acceleration, trajectories. In the general case, the problem of describing the motion of bodies is complex. It is especially difficult if the bodies are noticeably deformed in the process of movement. It is easier to describe the movement of the body, mutual arrangement parts of which do not change. Such a body is called absolutely solid. In fact, there are no absolutely rigid bodies. But in those cases when real bodies deform little during motion, they can be considered as absolutely rigid. (Another abstract model introduced when considering motion.) However, motion is also absolutely solid body in general, it turns out to be very difficult. Any complex motion of an absolutely rigid body can be represented as the sum of two independent motions: translational and rotational.
translational movement. The simplest motion of rigid bodies is progressive.
Translational called such a motion of a rigid body in which any segment connecting any two points of the body remains parallel to itself.
In translational motion, all points of the body make the same movements, describe the same trajectories, go through the same paths, have equal values ​​at each moment of time. speed and acceleration. Let's show it.
Let the body move forward ( fig.2.1). Connect two of its arbitrary points B and A segment. The distance does not change, since the body is absolutely rigid. During translational motion, the module and direction of the vector remain constant. As a result, the trajectories of the points B and A are the same, since they can be completely matched by parallel translation on the vector .

According to figure 2.1 moving points A and B are the same and take place at the same time. Therefore, the points A and B have the same speed and acceleration.
It is quite obvious that to describe the translational motion of a rigid body, it is sufficient to describe the motion of any one of its points. Only with translational motion can we talk about the speed and acceleration of the body. With any other movement of the body, its points have different speeds and acceleration, and the terms "velocity of the body" and "acceleration of the body" for non-translational motion lose their meaning.
Approximately progressively move the desk drawer, the pistons of the car engine relative to the cylinders, the cars in a straight section railway, the cutter of the lathe relative to the bed. Pedal movement of a bicycle or ferris wheel cab in parks ( fig.2.2, 2.3) are also examples of translational motion.

For description forward movement of a rigid body, it is enough to write the equation of motion of one of its points.

G.Ya.Myakishev, B.B.Bukhovtsev, N.N.Sotsky, Physics Grade 10

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