w o r m   s t ri n g s

By Henryk Szubinski

 

Angular momentum is a quantity that is useful in describing the rotational state of a physical system. For a rigid body rotating around an axis of symmetry (e.g. the fins of a ceiling fan), the angular momentum can be expressed as the product of the body’s moment of inertia and its angular velocity (\mathbf{L} = I \boldsymbol{\omega}). In this way, angular momentum is sometimes described as the rotational analog of linear momentum

loading the sequence of data on processess in the projective data systems of the process————>F

by a 1/3 uncertainty of the basics in projective estimations made by detailed recordings of the main field and its depth of perspective to which every such point would be a type multi vector disk type and its value of referenced connections by multi field rotations of large gravity disks by similar gravity and the data on the free flying objects responsible for the processess in which specific sections are connectable to a wave form STRING THEORY AS A MASS GALACTIC PLATFOR REPLICATING ITS DISKS IN A CONNECTED SEQUENCE RESULTANT in the solid form resembling a worm in its motion and also as such thebasic reasons for the accellerations of the larger internal sections with similar gravity increases as related to the core section values..

The data can be recorded and stored in the values registerred at the ends of the process as started and ended in the force as a waveform with the specifics of data being in the projective zones of angular momentum:

It is very often convenient to consider the angular momentum of a collection of particles about their centre of mass, since this simplifies the mathematics considerably. The angular momentum of a collection of particles is the sum of the angular momentum of each particle:

\mathbf{L}=\sum_i \mathbf{R}_i\times m_i \mathbf{V}_i

where Ri is the distance of particle i from the reference point, mi is its mass, and Vi is its velocity. The center of mass is defined by:

\mathbf{R}=\frac{1}{M}\sum_i m_i \mathbf{R}_i

where the total mass of all particles is given by

M=\sum_i m_i\,

It follows that the velocity of the centre of mass is

\mathbf{V}=\frac{1}{M}\sum_i m_i \mathbf{V}_i\,

If we define \mathbf{r}_i as the displacement of particle i from the centre of mass, and \mathbf{v}_i as the velocity of particle i with respect to the centre of mass, then we have

\mathbf{R}_i=\mathbf{R}+\mathbf{r}_i\,   and    \mathbf{V}_i=\mathbf{V}+\mathbf{v}_i\,

and also

\sum_i m_i \mathbf{r}_i=0\,   and    \sum_i m_i \mathbf{v}_i=0\,

so that the total angular momentum is

\mathbf{L}=\sum_i (\mathbf{R}+\mathbf{r}_i)\times m_i (\mathbf{V}+\mathbf{v}_i) = \left(\mathbf{R}\times M\mathbf{V}\right) + \left(\sum_i \mathbf{r}_i\times m_i \mathbf{v}_i\right)

The first term is just the angular momentum of the centre of mass. It is the same angular momentum one would obtain if there were just one particle of mass M moving at velocity V located at the centre of mass. The second term is the angular momentum that is the result of the particles moving relative to their center of mass. This second term can be even further simplified if the particles form a rigid body, in which case a spin appears. An analogous result is obtained for a continuous distribution of matter.