User:John R. Brews/Coriolis force: Difference between revisions

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The '''Coriolis force''' is a force experienced by a object traversing a path in a rotating framework that is proportional to its speed and also to the sine of the angle between its direction of movement and the axis of rotation. It is one of three such ''inertial forces'' that appear in an accelerating frame of reference due to the acceleration of the frame, the other two being the [[centrifugal force]] and the [[Euler force]]. The mathematical expression for the Coriolis force appeared in an 1835 paper by a French scientist [[Gaspard-Gustave Coriolis]] in connection with the theory of water wheels, and also in the [[Theory of tides|tidal equations]] of [[Pierre-Simon Laplace]] in 1778.
===Quarks===


Although sometimes referred to as an ''apparent'' force, it can have very real effects.
The quarks that may engage one another in reactions are determined by the [[Cabbibo-Kobayashi-Maskawa matrix]]:[http://books.google.com/books?id=f89yg8a1t-EC&pg=PA23&dq=Cabibbo+angle&hl=en&ei=XYZvToTqN7PZiAKM55juBg&sa=X&oi=book_result&ct=result&resnum=2&ved=0CDIQ6AEwATgK#v=onepage&q=Cabibbo%20angle&f=false Morii]
:<math>\begin{pmatrix}
d'\\
s'\\
b'\\
\end{pmatrix} = \begin{pmatrix}
U_{ud}&U_{us}&U_{ub}\\
U_{cd}&U_{cs}&U_{cb}\\
U_{td}&U_{ts}&U_{tb}\\
\end{pmatrix}=\begin{pmatrix}
d\\
s\\
b\\
\end{pmatrix} </math>


==Reference frames==
The quarks can be arranged to exhibit right- and left-handedness, subscripts ''L'' and ''R'', to resemble the leptons. The right-handed quarks do not couple to the weak interaction, and are labeled with subscript ''R''. The left-handed quarks corresponding to these right-handed quarks are mixtures of quarks. Thus, the up and down quarks are assembled as:
[[Classical_mechanics#Newton.27s_laws_of_motion|Newton's laws of motion]] are expressed for observations made in an inertial frame of reference, that is, in any frame of reference that is in straight-line motion at constant speed relative to the "fixed stars", an historical reference taken today to refer to the entire universe. However, everyday experience does not take place in such a reference frame. For example, we live upon planet [[Earth]], which rotates about its axis (an accelerated motion), orbits the [[Sun]] (another accelerated motion), and moves with the [[Milky Way]] (still another accelerated motion).


The question then arises as to how to connect experiences in accelerating frames with Newton's laws that are not formulated for such situations. The answer lies in the introduction of [[Inertial forces|''inertial forces'']], which are forces observed in the accelerating reference frame, due to its motion, but are not forces recognized in an inertial frame. These inertial forces are included in Newton's laws of motion, and with their inclusion Newton's laws work just as they would in an inertial frame. ''Coriolis force'' is one of these inertial forces, the other two being the centrifugal force and the Euler force.
:<math> \tbinom {u}{d}_L \ ; \ \ u_R,\ d_R \ .</math>


These motions are slight, but the Coriolis force does affect aiming artillery pieces and plotting transoceanic air flights. The way Coriolis forces work is illustrated below by a few examples.
The other generations are arranged similarly:


==References==
:<math> \tbinom {c}{s}_L \ ; \ \ c_R,\ s_R \ , </math>
<references/>
:<math> \tbinom {t}{b}_L \ ; \ \ t_R,\ b_R \ . </math>
{| class="wikitable" style="margin: 0 auto; text-align:center"
|+'''Right- and left-handed quarks'''
! Symbol
! Electric charge, ''Q''
! Weak isospin, (''I<sub>W</sub>, I<sub>W3</sub>'')
! Weak hypercharge, (''Y<sub>W</sub>'')
|-
| ''u<sub>L</sub>, c<sub>L</sub>, t<sub>L</sub>''
| +2/3
| (1/2, +1/2)
| +1/3
|-
| ''d<sub>L</sub>, s<sub>L</sub>, b<sub>L</sub>''
| −1/3
| (1/2, −1/2)
| +1/3
|-
| ''u<sub>R</sub>, c<sub>R</sub>, t<sub>R</sub>''
| +2/3
| 0
| +4/3
|-
| ''d<sub>R</sub>, s<sub>R</sub>, b<sub>R</sub>''
| −1/3
| 0
| −2/3
|-
|}
 
 
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Latest revision as of 04:07, 22 November 2023


The account of this former contributor was not re-activated after the server upgrade of March 2022.


Quarks

The quarks that may engage one another in reactions are determined by the Cabbibo-Kobayashi-Maskawa matrix:Morii

The quarks can be arranged to exhibit right- and left-handedness, subscripts L and R, to resemble the leptons. The right-handed quarks do not couple to the weak interaction, and are labeled with subscript R. The left-handed quarks corresponding to these right-handed quarks are mixtures of quarks. Thus, the up and down quarks are assembled as:

The other generations are arranged similarly:

Right- and left-handed quarks
Symbol Electric charge, Q Weak isospin, (IW, IW3) Weak hypercharge, (YW)
uL, cL, tL +2/3 (1/2, +1/2) +1/3
dL, sL, bL −1/3 (1/2, −1/2) +1/3
uR, cR, tR +2/3 0 +4/3
dR, sR, bR −1/3 0 −2/3