You get a bonus - 1 coin for daily activity. Now you have 1 coin

3.8. Center of Inertia System

Lecture




  3.8.  Center of Inertia System

In the above Newton's equation, it was assumed that the body is so small in size that it can be considered a material point. The motion of any non-deformable body of finite size can be described by equations similar to (3.6), if we introduce the concept of "center of mass" ("center of inertia") of the body. If the body consists of n material points with masses   3.8.  Center of Inertia System and radius vectors   3.8.  Center of Inertia System then the center of mass of the system of material points is called such a CC, the radius vector of which is defined as follows:

  3.8.  Center of Inertia System (3.7)

Where   3.8.  Center of Inertia System and   3.8.  Center of Inertia System is the mass and radius-vector of the i-th point of the system, m is the total mass of the system.

Accordingly, the relations between the Cartesian coordinates of the center of inertia and all points of the system have the form:

  3.8.  Center of Inertia System

Inertia center speed:

  3.8.  Center of Inertia System (3.8)

Impulse system The geometric sum of the impulses of all material points of the system is called the impulse of the system and is denoted by the letter   3.8.  Center of Inertia System :

  3.8.  Center of Inertia System ,

then the center of mass velocity

  3.8.  Center of Inertia System (3.9)

Thus, from (3.9) it follows that the impulse of the system is equal to the product of the mass of the entire system and the speed of its center of inertia:

  3.8.  Center of Inertia System (3.10)

Ads:

Comments


To leave a comment
If you have any suggestion, idea, thanks or comment, feel free to write. We really value feedback and are glad to hear your opinion.
To reply

Physical foundations of mechanics

Terms: Physical foundations of mechanics