One of the basic physical principles of the interaction of solid bodies is the law of inertia, formulated by the great Isaac Newton. We encounter this concept almost constantly, since it has an extremely great influence on all material objects of our world, including humans. In turn, such a physical quantity as the moment of inertia is inextricably linked with the law mentioned above, determining the strength and duration of its impact on solid bodies.
From the point of view of mechanics, any material object can be described as an unchanging and clearly structured (idealized) system of points, the mutual distances between which do not change depending on the nature of their movement. This approach makes it possible to accurately calculate the moment of inertia of almost all solid bodies using special formulas. Another interesting nuance here isthe fact that any complex, having the most intricate trajectory, movement can be represented as a set of simple movements in space: rotational and translational. This also makes life much easier for physicists when calculating this physical quantity.
To understand what is the moment of inertia and what is its influence on the world around us, it is easiest to use the example of a sharp change in the speed of a passenger vehicle (braking). In this case, the legs of a standing passenger will be dragged along by friction on the floor. But at the same time, no impact will be exerted on the torso and head, as a result of which they will continue to move at the same specified speed for some time. As a result, the passenger will lean forward or fall. In other words, the moment of inertia of the legs, extinguished by the force of friction on the floor, will be significantly less than the rest of the points of the body. The opposite picture will be observed with a sharp increase in the speed of a bus or tram car.
The moment of inertia can be formulated as a physical quantity equal to the sum of the products of elementary masses (those individual points of a solid body) and the square of their distance from the axis of rotation. It follows from this definition that this characteristic is an additive quantity. Simply put, the moment of inertia of a material body is equal to the sum of similar indicators of its parts: J=J1 + J2 + J3 + …
This indicator for bodies of complex geometry is found experimentally. account fortake into account too many different physical parameters, including the density of an object, which can be inhomogeneous at different points, which creates the so-called mass difference in different segments of the body. Accordingly, the standard formulas are not suitable here. For example, the moment of inertia of a ring with a certain radius and uniform density, having an axis of rotation that passes through its center, can be calculated using the following formula: J=mR2. But in this way it will not be possible to calculate this value for a hoop, all parts of which are made of different materials.
And the moment of inertia of a ball of solid and homogeneous structure can be calculated by the formula: J=2/5mR2. When calculating this indicator for bodies relative to two parallel axes of rotation, an additional parameter is introduced into the formula - the distance between the axes, denoted by the letter a. The second axis of rotation is denoted by the letter L. For example, the formula may look like this: J=L + ma2.
Careful experiments on the study of the inertial motion of bodies and the nature of their interaction were first made by Galileo Galilei at the turn of the sixteenth and seventeenth centuries. They allowed the great scientist, who was ahead of his time, to establish the basic law on the preservation by physical bodies of a state of rest or rectilinear motion relative to the Earth in the absence of other bodies acting on them. The law of inertia became the first step in establishing the basic physical principles of mechanics, which at that time were still completely vague, indistinct and obscure. Subsequently, Newton, formulating the general laws of motionbodies, included among them the law of inertia.
