Moment of momentum: features of rigid body mechanics

Moment of momentum: features of rigid body mechanics
Moment of momentum: features of rigid body mechanics
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Momentum refers to the fundamental, fundamental laws of nature. It is directly related to the symmetry properties of the space of the physical world in which we all live. Thanks to the law of its conservation, the angular momentum determines the physical laws that are familiar to us for the movement of material bodies in space. This value characterizes the amount of translational or rotational movement.

angular momentum
angular momentum

Moment of momentum, also called "kinetic", "angular" and "orbital", is an important characteristic that depends on the mass of a material body, the features of its distribution relative to an imaginary axis of circulation and the speed of movement. Here it should be clarified that in mechanics rotation has a broader interpretation. Even a rectilinear motion past some point arbitrarily lying in space can be considered rotational, taking it as an imaginary axis.

The angular momentum and the laws of its conservation were formulated by Rene Descartes in relation to a progressively moving system of material points. True, he did not mention the preservation of rotational motion. Only a century later, LeonardEuler, and then another Swiss scientist, physicist and mathematician Daniil Bernoulli, while studying the rotation of a material system around a fixed central axis, concluded that this law also applies to this type of movement in space.

Angular moment of a material point
Angular moment of a material point

Further studies fully confirmed that in the absence of external influence, the sum of the product of the mass of all points by the total speed of the system and the distance to the center of rotation remains unchanged. Somewhat later, the French scientist Patrick Darcy expressed these terms in terms of the areas swept by the radius vectors of elementary particles over the same period of time. This made it possible to connect the angular momentum of a material point with some well-known postulates of celestial mechanics and, in particular, with the most important position on the motion of the planets by Johannes Kepler.

Momentum of a rigid body
Momentum of a rigid body

The angular momentum of a rigid body is the third dynamic variable to which the provisions of the fundamental conservation law are applicable. It states that, regardless of the nature and type of movement, in the absence of external influence, a given quantity in an isolated material system will always remain unchanged. This physical indicator can undergo any changes only if there is a non-zero moment of the acting forces.

From this law it also follows that if M=0, any change in the distance between the body (system of material points) and the central axis of rotation will certainly cause an increase or decreasethe speed of its revolution around the center. For example, a gymnast performing somersaults in order to make several turns in the air initially rolls her body into a ball. And ballerinas or figure skaters, while pirouetted, spread their arms to the sides if they want to slow down the movement, and, conversely, press them to the body when they try to spin at a faster speed. Thus, the fundamental laws of nature are used in sports and art.

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