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The concept of a perfectly rigid body. Torque and moment of inertia. The basic law of dynamics of rotational motion

The concept of a perfectly rigid body. Torque and moment of inertia. The basic law of dynamics of rotational motion.

Absolutely solid тíло — the body, which under any circumstances is not deformed and under all conditions the distance between two points (or more precisely between the two parts) which remains constant.

   A rigid body can be considered as a system of material points. For a complete description of the motion of a single point it is necessary to know its three coordinates, therefore, for N points the number of required coordinates, and therefore, and the number of equations for their determination would be 3N. The number N can be arbitrarily large, the rigorous solution of the system  of 3N equations  very limited.

 

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Additionally, the nature of the movement of the body as a whole may be different. There are generally progressive, rotational and plane motion. When translational motion all points move on parallel trajectories, so to describe the motion of the body in General enough to know the law of motion of a single point. In particular, this point can serve as the center of mass of a rigid body. In this case the problem of describing the motion of a body boils down to  theorem about the center of mass motion. In the rotational motion, all points of the body describe concentric circles, the centers of which lie on the same axis. Speed  points on each of the circles SV’connected with the radii of these circles and the angular rotation speed of:Solid body rotation retains its shape, therefore, the radii of rotation remain constant.

Abstraction of rigid bodies convenient when considering rotational motion. Real bodies deform during rotation. The magnitude of this deformation depends on the speed of rotation and the properties of the body. If you rotate magaraci on UMTS, the significant deformation, in the case of metal parts of mechanisms — small, and it can be neglected.

In the rotational motion the inertia of a body depends on its mass relative to the axis of rotation. The farther from the axis the mass is located, the greater its inertia.

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