Thursday, July 14, 2016

No Sustained "Bood"

From the post "Just When You Think c Is The Last Constant" dated 26 Jun 2016, we have,

\(c=\sqrt { \cfrac { S_{ n }(32\pi ^{ 4 }-1) }{ 64\pi .\theta _{ \psi  }ln(cosh(\theta _{ \psi  }))tanh(\theta _{ \psi  }) } *\left( \cfrac { \theta _{ \psi  } }{ 0.7369 }  \right) ^{ 3 } } \)

when we replace \(\cfrac{77}{2}=S_n\).

When \(S_n\) is variable,

\(v=\sqrt { \cfrac { S_{ n }(32\pi ^{ 4 }-1) }{ 64\pi .\theta _{ \psi  }ln(cosh(\theta _{ \psi  }))tanh(\theta _{ \psi  }) } *\left( \cfrac { \theta _{ \psi  } }{ 0.7369 }  \right) ^{ 3 } } \) --- (1)

and

\(S_n=39-\cfrac{0.5S}{\omega_o}v\) --- (2)

where \(S\) is a constant.  From the post "An Egg With Bood..." dated 12 Jul 2016,

\(\omega^2=\cfrac{F_{drag}}{\delta m}\cfrac{sin(\theta)}{r}\)

at the front tip of the particle, \(r\rightarrow 0\) and \(\theta\rightarrow 0\).  If we assume

\(\lim\limits_{r,\,\theta\rightarrow 0}{\cfrac{sin(\theta)}{r}}=1\)

at the tip of the particle,

\(\omega^2_t=\cfrac{F_{drag}}{\delta m}\)

Since, \(F_{drag}\propto v^2\)

\(\omega^2_t=T_t.v^2\) --- (3)

where \(T_t\) is a constant.  The particle spin, \(\omega_t\) decreases with decreasing \(v\).

When \(v\) increases under the action of an attractive field \(F.c\), \(S_n\) according to expression (2) decreases, which through expression (1) decreases \(v\).  As \(v\) decreases \(\omega_t\) decreases via (3).  But under the action of the field, \(v\) increases again.  It seems that the cycle repeats but this is not a sustained oscillation.  Energy in the spin of the particle is not being exchanged for translational kinetic energy in \(v\) and vice versa.  \(S_n\) presents a lower values because the face that presents a higher number of basic particles towards the attractive field, is being turn away by spin.  As the particle spins, \(S_n\) represents the average number of basic particles on one side of the big particle for which they constitute.

This is just a short burst of EB, before \(\omega_t\) settles to a constant value.

Substitute (3) into (1)

\( \omega _{ t }=\sqrt { \cfrac { S_{ n }T_{t}(32\pi ^{ 4 }-1) }{ 64\pi .\theta _{ \psi  }ln(cosh(\theta _{ \psi  }))tanh(\theta _{ \psi  }) } *\left( \cfrac { \theta _{ \psi  } }{ 0.7369 }  \right) ^{ 3 } } \)

given \(T_t\) which is a constant, \(\omega_t\) is determined.  The particle can spin with constant \(\omega_t\) and travel at a speed lower than \(c_{39}\).

All that is presented here is under the assumption that \(c\), light speed is a constant.