may the force be with you! - sjtuweiwang/sites/www... · 2019. 5. 16. · weak force • weak force...
TRANSCRIPT
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May the force be with you!
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Fundamental vs. non-fundamental force
TosolveNewton’smechanicsproblems,oneneedtoknowforces.Therearefourfundamentalforces:Thegravita=onalforcelawfoundbyNewtonisfundamental.Bynow,allfundamentallawsofotherthreeforcesareknownaswell:electromagne=c,weakandstrong.
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Friction
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The E&M force: Coulomb’s law
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Strong force
• Strongforceistheonethatbindstogethertheneutronsandprotonsinnuclei.• Thisfundamentalforcewasfinallyunderstoodin1970swhencolorchargeandatheoryofcolorinteractionsareproposedandverified.(Chromodynamics)• However,solvingthe“NewtonEquation”isveryverydifficulty.Theonlywaytodothisisusingalargescalecomputer!
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Weak force
• Weakforceistheonethatchangestheprotonintoaneutronandhenceamongdifferentelements.• Weakforceisthefirststepinthesunburning.• Thefundamentaltheoryofweakforcewasproposedin1967,wasverifiedovertheyears.• Theweakforcehasthesameoriginastheelectromagneticforce.• Theweakforcealsogivethemasstotheelectron!
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Pseudo force due to non-inertial frame• Ininertialframes,alltheforcesare“physical”.Alllawsininertialframesarethesame.• However,whenworkinginnon-inertialframe,thereareextraforcesinNewton’sequation.Forexamplewhenaframeisacceleration,oneneedstotakeintoaccountthisspurious“force”• Sometimeunavoidable.LiketheCoriolisforceontheEarth->Foucaultpendulum.
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Question
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Question
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Braess' paradox
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Coordinates transformation
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Coordinate translation
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Translation
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Translational invariance
• Thenewton’slawofphysicsisvariantundertranslation
• Theforcedoesnotchangeundertranslation
• Theaccelerationdoesnotchangeundertranslation
• Thisistheoriginofmomentumconservation
• Webelievealllawsofphysicsareinvariantunder
translation
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Time translational symmetry
•
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Rotations
11 12 13
21 22 23
31 32 33
'''
x a a a xy a a a yz a a a z
⎛ ⎞ ⎛ ⎞⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟=⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠
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Rotational matrix
•
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Rotational symmetry
•
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Galileo transformation
• Twocoordinatesarerelatedbyconstantspeed,sowehavetwocoordinates
ThisiscalledGalileantransformation.
0
0
0
'''
'
x
y
z
t tx x v ty y v t
z z v t
=
= −
= −
= −
0
''t tr r v t=
= −! ! !
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Newton’s equations are invariant under Galileo transformation
• Galileanprincipleofrelativity.Nottruewhenvelocityislarge
0
''t tr r v t=
= −! ! ! 0 0dv
dt=
!'a a=! !
'F F=! !
F ma=! ! ' 'F ma=
! !