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

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==Meteorology==
===Quarks===
{{Image|Wind deflection.PNG|left|250px|Wind motion in direction of pressure gradient is deflected by the Coriolis force by an amount dependent upon latitude, less closer to the equator and most at the poles.}}
{{Image|Low pressure pattern in northern hemisphere.PNG|right|200px|In the northern hemisphere, Coriolis force deflects winds flowing into a low pressure region to form a counterclockwise flow.}}
A pressure gradient in the atmosphere is equalized by driving a wind along the pressure gradient. However, from the viewpoint of meteorology, the motion is observed most naturally within the reference frame of a rotating Earth. As pointed out just above and in the figure to the left, in the Earth's reference frame any motion is affected by a Coriolis force, as given by:


:<math> \boldsymbol{ v} = \begin{pmatrix} v_e \\ v_n\end{pmatrix}\ ,</math> &nbsp; &nbsp; <math>\boldsymbol{ a_{Cor}} = \begin{pmatrix} v_n \\ -v_e\end{pmatrix}\ f\ , </math>
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>


where ''f'' = {{nowrap|2''&omega;'' sin''&phi;''}} is the Coriolis parameter. Consequently, the wind takes an apparent direction deflected to the right of the pressure gradient in the northern latitudes, and to the left in the southern latitudes. The Coriolis parameter is a maximum at the poles, zero at the equator and flips sign as one crosses form the northern to southern hemispheres, as indicated in the figure.
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:


One consequence is that a low pressure region that sucks air into it, as shown in the figure, results in a counterclockwise flow of winds in the northern hemisphere (called a cyclone) because of the Coriolis force.<ref name = Todd>
:<math> \tbinom {u}{d}_L \ ; \ \ u_R,\ d_R \ .</math>


For further discussion see {{cite book |title=An Introduction to Physical Science |author=James T. Shipman, Jerry D. Wilson, Aaron Todd |url=http://books.google.com/books?id=1LvMLoaN0HQC&pg=PA557 |pages=pp. 557 ''ff'' |year=2007 |edition = 12th ed |isbn=0618935967 |publisher=Cengage Learning}}
The other generations are arranged similarly:


</ref>
:<math> \tbinom {c}{s}_L \ ; \ \ c_R,\ s_R \ , </math>
:<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
|-
|}


==Notes==
<references/>


Contributed by myself in June 2008, for example, [http://en.wikipedia.org/w/index.php?title=Coriolis_effect&diff=218224145&oldid=218221895 here] [http://en.wikipedia.org/w/index.php?title=Coriolis_effect&diff=218199099&oldid=218197139 here], [http://en.wikipedia.org/w/index.php?title=Coriolis_effect&diff=219110044&oldid=219105420 added Limerick]
{{Reflist}}
 
 
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http://books.google.com/books?id=imrm2aOs9_8C&pg=PA90&dq=Foucault+pendulum&hl=en&ei=34ZgTeukEIuesQPMvPHYCA&sa=X&oi=book_result&ct=result&resnum=7&ved=0CEQQ6AEwBjge#v=onepage&q=Foucault%20pendulum&f=false
 
[http://books.google.com/books?id=d3kqAAAAMAAJ&pg=PA160&dq=Foucault+pendulum&hl=en&ei=34ZgTeukEIuesQPMvPHYCA&sa=X&oi=book_result&ct=result&resnum=8&ved=0CEkQ6AEwBzge#v=onepage&q=Foucault%20pendulum&f=false Maxwell]
 
http://books.google.com/books?id=wr2QOBqOBakC&pg=PA184&dq=Foucault+pendulum&hl=en&ei=U4hgTd-9Foa6sQP3lt3ACA&sa=X&oi=book_result&ct=result&resnum=2&ved=0CDAQ6AEwATgy#v=onepage&q=Foucault%20pendulum&f=false
 
[http://books.google.com/books?id=erkWAAAAYAAJ&pg=PA241&dq=Foucault+pendulum&hl=en&ei=CV1gTenZOpGisQO9ruzNCA&sa=X&oi=book_result&ct=result&resnum=6&ved=0CFEQ6AEwBQ#v=onepage&q=Foucault%20pendulum&f=false Practical matters]
 
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==References==
<references/>

Latest revision as of 03:07, 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