Rolling Movement
Introducción
In the field of physics they have studied the dynamics for particles or also for a system of "n" point particles in which a displacement can manifest themselves in a relative manner, which in turn is important to know that It refers to the moment of rotation, where this implies both the force carried out and the distance to the point of rotation, which is linked to both. Now, dear reader, the most unique thing about all this is to take into account in a simple way to refer to the moment dynamic, in the most dynamic way this is called the moment of a force with respect to a given point and a vector quantity, defined by the vector product of the position vector of the point of application of the force, specified with respect to the point at which it is taken the moment is defined by the force vector. As the distance to the turning point, which links both, now, dear reader, the most unique of all this, take into account in a simple way to have a reference to dynamic moment, for this opportunity at the moment of inertia in parallel axis , where the moment of inertia of any object on an axis through its center of mass is the minimum moment of inertia on an axis in that direction of space.
For the case of Steiner's Parallel Axis Theorem, where the moment of inertia about a parallel axis is considered, defined by the sum of the moment of inertia of the object, a flat body or having characteristics of plane bodies of form geometric, on its center of mass, through the same crossing between the object and its perpendicular plane.
A Rolling movement
In this type of movement it refers to how a wheel body undergoes a translation making it rotate around the center of mass, an example of the moment of inertia will not vary the gravity in the period of oscillation and the experimental calculation of the moment of inertia will give The same result usually associates celestial bodies such as the earth and the moon with this movement, since it is a type of movement that combines the rotation of an object or body axially symmetrically and the action of a movement phenomenon under the scheme of the translation with respect to a surface and that implies that the body that rolls on the surface does it without slipping, zero speed with respect to the surface.
In this representation of a spherical body we observe its radius R, which moves along a plane with angular velocity w, such that its center of mass has a translation speed com, so vcm = Rw will be fulfilled, where O is the instantaneous imaginary axis of rotation which in turn passes through 0.
The moment of inertia is represented by this mathematical model: I = Icm + m. R ^ 2, everything comes from the following relation when the cylinder-shaped body rotates a certain angle dθ, the center of it experiences a displacement dx; the relationship between these two quantities is: dx = dθ R.
The other points of the cylinder will have at that moment a certain speed, perpendicular to the instantaneous axis of rotation and to the line that joins said particle with said axis and with a module proportional to said distance. For the calculation of kinetic energy from the point of view: Ec = 1/2. I. W ^ 2, where I being the moment of inertia with respect to the instantaneous axis of rotation, we must bear in mind the following, dear reader, that in the field of physics there is a strong relationship between the magnitudes proper to translational movement and the magnitudes characteristic of rotation movement due to their similarities, since the moment of inertia takes into account the geometry of the system, thanks to the fact that the particle system will depend on how the different particles are distributed in space and the axis of rotation.
[1]-Solved problems of centers of gravity and moments of inertia By Manuel Forner Gumbau, 2006.
[2]-Physics for science and technology. Me by Paul Allen Tipler, Gene Mosca, 2004.
