Translational motion is the mechanical movement of a system of points ( absolutely solid ), in which a straight line segment 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 point in time [1] . During translational motion, all points of the body describe the same trajectory (up to a constant displacement in space) and at any given moment in time they have the same direction and absolute magnitude of the velocity and acceleration vectors that change synchronously for all points of the body.
In the general case, the translational movement occurs in three-dimensional space, but its main feature - the preservation of parallelism of any segment to itself, remains valid.
Mathematically progressive movement in its final result is equivalent to parallel transfer . However, regarded as a physical process, it is a variant of helical motion in three-dimensional space (see Fig. 2).
Content
The basic law of the dynamics of translational movement
The time derivative of the momentum of a material point or system of material points relative to a fixed (inertial) reference frame is equal to the main vector of all external forces applied to the system.
Translational examples
For example, the elevator car moves progressively. Also, in a first approximation, translational movement is made by the cabin of the Ferris wheel [2]
To a first approximation (if we neglect the swing of the foot), the forward pedal performs the bicycle pedal, which performs one turn around its axis during the full cycle of its stroke.
The relationship between the movement of the body and the movement of its points
If the body moves progressively, then to describe its motion it is enough to describe the motion of its arbitrary point (for example, the motion of the center of mass of the body).
One of the most important characteristics of a pointβs movement is its trajectory , which in the general case is a spatial curve that can be represented as conjugate arcs of different radii emanating from each of its centers, the position of which can change in time. In the limit, the straight line can be considered as an arc, the radius of which is equal to infinity .
In this case, it turns out that during translational movement at any given moment in time, any point on the body rotates around its instantaneous center of rotation, and the length of the radius at the moment is the same for all points on the body. The velocity vectors of the points of the body, as well as the accelerations they experience, are identical in magnitude and direction.
When solving problems of theoretical mechanics, it can be convenient to consider the motion of a body as the addition of the motion of the center of mass of the body and the rotational motion of the body itself around the center of mass (this fact was taken into account when formulating the Koenig theorem ).
Device Examples
The principle of translational motion is implemented in a drawing device - a pantograph , the leading and trailing arms of which always remain parallel, that is, they move forward. Moreover, any point on the moving parts in the plane makes the specified movements, each around its instantaneous center of rotation with the same angular velocity for all moving points of the device.
It is significant that the leading and trailing arm of the device, although moving in accordance, are two different bodies. Therefore, the radii of curvature along which the given points on the leading and trailing shoulders move can be made unequal, and this is precisely the point of using a device that can reproduce any curve on a plane in a scale determined by the ratio of shoulder lengths.
In fact, the pantograph provides a synchronous translational movement of the system of two bodies: the βreaderβ and the βwriterβ, the movement of each of which is illustrated by the above drawing.
See also
- Centripetal and centrifugal forces
- Clan mechanism
Notes
- β By definition, a certain body is called changing its shape if the distance between its points does not remain constant. With such a body can not be associated with any constant along the length of the segment, always oriented in space. Therefore, a progressively moving body can be considered ( kinematically ) absolutely solid , although it can be a liquid drop, a gas cloud, or a star cluster .
- β Strictly speaking, the movement of the cab of the Ferris wheel can be considered progressive only in the limit of the infinitely slow rotation of the wheel, since rotational acceleration leads to small deviations of the suspended cab from the vertical.
Literature
- Newton I. Mathematical principles of natural philosophy. Per. and approx. A.N. Krylova. M .: Nauka, 1989.
- S. E. Khaikin. Inertia forces and weightlessness. M .: Nauka, 1967.
- Frisch S.A. and Timoreva A.V. Course in General Physics, Textbook for Physics and Mathematics and Physics and Technology Faculties of State Universities, Volume I. M.: GITTL, 1957.
- Translational motion // Physical Encyclopedic Dictionary / Ch. ed. A.M. Prokhorov . - M .: Soviet Encyclopedia, 1983. - S. 579. - 928 p. - 100,000 copies.
Links
- V.I. Gervids. Translational and rotational movements (flash). NRNU MEPhI (03/10/2011). - Physical demonstrations. Date of treatment December 19, 2011.