Care must be taken when talking about momentum, so as not to get confused. Its correct meaning is quantity of motion and can differentiate into linear or angular.
Let's start with linear momentum. Newton laid the foundation for dynamics, the mathematical theory of motion, by understanding that the natural behavior of bodies involves them moving in a straight line at constant velocity. He defined linear momentum as the product of a body's mass times its velocity, which in turn is defined as the velocity in a particular direction. In fact, if a certain amount of force is exerted on a body, it acquires velocity toward a direction, and furthermore, the momentum generated cannot be stopped unless the moving body is slowed or restrained by external forces. This concept is encapsulated in a fundamental law of nature, called the Law of conservation of linear momentum.
The linear momentum is thus a property of an object that is in motion and changes position relative to a fixed point of reference, moving along a straight line. Whereas, if the object changes not only position but also direction with respect to the reference point, starting to rotate on itself, we refer to angular momentum. Here we find the Law of conservation of angular momentum, which is the rotational equivalent of the Law of Conservation of Linear Momentum.
Consider a dancer. By running, jumping or simply dropping her weight toward a direction, she generates potential linear momentum in which her body creates effortless motion. Instead, if before or during the action the dancer gives a muscular impulse to change her direction, she begins to generate rotational momentum that causes her to rotate on herself, acquiring what is known as angular momentum. Pirouettes and turns are great examples of this.
But what does it really mean to use momentum? Let's assume that as we prepare for a day-long car trip, we would like to be prepared to meet our body's required needs, such as thirst. We would probably carry with us a bottle containing enough water to make use of it during the day. Well, speaking of dance, replace water with momentum and we will have a valid analogy. When we dance there are movements in which potential linear or rotational momentum is generated, but rather than using it in that instant, we can conserve it to use it at a later time.
Consider running as an example, as far as linear momentum is concerned. If we let our body fall forward, we have already generated a potential linear momentum. In this case, to conserve momentum we can repel our falling weight step by step, letting the action evolve into a run. The more we let our weight fall forward, the more the run increases in speed. By conserving this momentum, we have the opportunity to use it later, for example by directing it in the explosive creation of a jump, or other movements.
Now let us turn to angular momentum, taking fouettés as an example. At each plié the push of the ground foot generates new force to create rotational motion. In physics we can call this pushing action torque: a force that tends to create rotation. Meanwhile, the leg supported to the side carries a significant mass also generating rotational motion, in cooperation with the ground foot. Much of that mass is carried away from the vertical axis of rotation, causing the moment of inertia to increase while the angular velocity decreases. Here, it is mainly in that leg that momentum can be conserved and used later. The same happens in the arms. Thus, when the dancer during fouettés exploits the torque again, and brings the leg and arms closer to her, she gains new energy, rotating faster; the moment of inertia decreases, and the velocity increases.
Talking about dance, we can say that momentum is a flow of motion that the body does not resist, but allows its natural dynamics. It originates from a muscle impulse, which can be a release action or a certain amount of force used to initiate the movement. Muscle impulses can also be used during the action, to bounce the flow of movement in one direction or another. It is then possible to harness same momentum energy to create one or more movements. Action is also spiritually rooted in the human being's ability to let go and to recognize instead when the time is right to take action.
In American modern dance in the early 1900s, to detach themselves from the research of an artefactual movement, dancers began to visualize movement as a dynamic flow of energy, placing more importance on what lies between positions rather than on the positions themselves. The discovery of movement as the building block of dance, in the same way that sound is the building block of music, is one of the four important discoveries of modern dance. Awareness of momentum thus becomes a key component, enabling the dancer to feel movement as a dynamic flow, while at the same time moving the body efficiently.
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I link below an interesting video about momentum during fouettés!
Written by Matteo Mascolo.
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Translations: Text translated into English by Alberto Rabachin and Bianca Pasquinelli, into Spanish by Matteo Mascolo.
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Sources: The information is based on my personal learning about physics and movement.