User:
Newton's Principles for Rotation
Storyboard 
Newton's principles are stated for what is translation, however, because of the analogy between translation and rotation, they can also be formulated for what is rotation.
In that case the role of the moment is assumed by the angular momentum, that of the mass, the moment of inertia and that of the force, the so-called torque.
ID:(756, 0)
Rotation Generation
Image
Up until now, we have explored how force results in translation, but we haven't yet delved into how rotation is generated.
From the previous discussion, it can be concluded that any force $\vec{F}$ can be decomposed into two components. The first component, $\vec{F}{\parallel}$, lies along the line connecting the point of application (PA) to the center of mass (CM) of the object. The second component is $\vec{F}{\perp}$, which is perpendicular to the line connecting the point of application to the center of mass.
The first component causes the translation of the object, while the second component gives rise to its rotation.
ID:(322, 0)
Newton's Laws for the Rotation
Description
Due to the relationship between force and torque, it becomes possible to formulate the laws of rotation based on Newton's principles. Therefore, a connection should exist between the following concepts:
Principle 1
A constant moment > corresponds to a constant angular momentum.
Principle 2
A force: Change in momentum over time > corresponds to a torque: Change in angular momentum over time.
Principle 3
A reaction force > corresponds to a reaction torque.
ID:(1073, 0)
Angular Momentum
Equation
The moment ($p$) was defined as the product of the inertial Mass ($m_i$) and the speed ($v$), which is equal to:
| $ p = m_i v $ |
The analogue of the speed ($v$) in the case of rotation is the instantaneous Angular Speed ($\omega$), therefore, the equivalent of the moment ($p$) should be a the angular Momentum ($L$) of the form:
 $ L = I \omega $ |
.
the inertial Mass ($m_i$) is associated with the inertia in the translation of a body, so the moment of Inertia ($I$) corresponds to the inertia in the rotation of a body.
ID:(3251, 0)
Angular momentum and moment relationship
Equation
Similar to the relationship that exists between linear velocity and angular velocity, represented by the equation:
| $ v = r \omega $ |
we can establish a relationship between angular momentum and translational momentum. However, in this instance, the multiplying factor is not the radius, but rather the moment. The relationship is expressed as:
| $ L = r p $ |
.
ID:(1072, 0)
Moment of inertia of a particle
Equation
For a particle with mass $m$ orbiting around an axis at a distance equivalent to a radius $r$, the relationship can be established by comparing the angular momentum expressed in terms of the moment of inertia and in terms of the moment, which is equal to:
| $ I = m r ^2$ |
La relación entre momento angular y momento es igual a
| $ L = r p $ |
se puede igualar a
| $ L = I \omega $ |
que tras remplazar
| $ p = m_i v $ |
y
| $ v = r \omega $ |
se puede concluir que la momento de inercia de una partícula girando en una órbita es
| $ I = m r ^2$ |
.
ID:(3602, 0)
Angular momentum and moment relationship
Equation
Similar to the relationship between the speed ($v$) and the angular Speed ($\omega$) with the radius ($r$), represented by the equation:
| $ v = r \omega $ |
we can establish a relationship between the angular Momentum ($L$) and the moment ($p$) in the context of translation. However, in this instance, the multiplicative factor is not the arm ($r$), but rather the moment ($p$). The relationship is expressed as:
| $ L = r p $ |
ID:(9874, 0)
0
Video
Video: Newton's Principles for Rotation