# Moment of inertia.

One of the basic physical principles of interaction of solids is the law of inertia, formulated by the great Isaac Newton.With this concept we face almost constantly, as it has a very big influence on all the material things of the world, including on human rights.In turn, the physical quantity such as the moment of inertia, is inextricably linked with the above-mentioned law, to determine the strength and duration of its effect on the solids.

In terms of the mechanics of any material object can be described as steadfast and clearly structured (idealized) system of points, the mutual distances between them do not change depending on the nature of their movement.This approach allows you to accurately calculate the special formulas for the moment of inertia of almost all solids.Another interesting nuance here is that any complex having the most intricate path, the movement can be represented as a set of simple movements in space: rotational and translational.It is also much easier life physicists in the calculation of the physical quantity.

understand, what is the moment of inertia, and what is its impact on the world around us, the easiest example of an abrupt change in the speed of a passenger vehicle (braking).In this case, the legs standing passenger friction entice floor behind him.But while the trunk and the head exerted no effect will not, so that they for some time will continue to move with the same predetermined speed.As a result, the passenger leaning forward or fall.In other words, the moment of inertia of the leg canceled by the friction force on the floor will be considerably less than the other points of the body.The opposite pattern is observed with a sharp increase in the speed of the bus or the tram car.

moment of inertia can be expressed as a physical quantity, equal to the sum of the masses of the elementary works (those individual points of a rigid body) by the square of their distance from the axis of rotation.From this definition, it follows that this characteristic is a value addition.Simply put, the moment of inertia of the material body is the sum of its parts similar indicators: J = J1 + J2 + J3 + ...

The indicator for the bodies of complex geometry is experimentally.It is necessary to consider too many different physical parameters, including the density of the object, which may be heterogeneous in its different points, which creates a so-called difference in the masses of the different body segments.Accordingly, standard formulas are not suitable.For example, the moment of inertia of the ring with a certain radius and uniform density, having a rotation axis that passes through its center, can be calculated using the following formula: J = mR2.But in this way will not calculate this value for the hoop, all parts of which are made of different materials.

A moment of inertia of the ball solid and homogeneous structure can be calculated by the formula: J = 2 / 5mR2.In the calculation of this indicator for the bodies relative to two parallel axes of rotation in the formula introduced an additional parameter - the distance between the axes are indicated as well.The second axis of rotation is designated with the letter L. For example, the formula may be as follows: J = L + ma2.

Careful experiments on the inertial movement of bodies and their interaction were first made by Galileo at the crossroads of the sixteenth and seventeenth centuries.They allowed the great scientist, ahead of his time, to establish the basic law of the preservation of physical bodies at rest or rectilinear motion relative to the Earth in the absence of exposure to other bodies.The law of inertia is the first step in establishing the basic physical principles of mechanics, while still quite vague, vague and ambiguous.Later, Newton formulating general laws of motion of bodies, included in their number and the law of inertia.