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Lecture_35

Lecture_35 - PHYS 342 Fall 2011 Lecture 35 Relativistic...

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PHYS 342 Fall 2011 Lecture 35: Relativistic Velocity Transformations Ron Reifenberger irck anotechnology Center Birck Nanotechnology Center Purdue University Lecture 35 1
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How do velocities transform? ˆ ˆˆ '' ' ' ' ' ' u i u j u k v f S’ x yz uu  ' u y S y’ ? u moving bject x x’ object z z 2
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Velocity transformation – along direction of relative motion '' ' f xx v t yy    ' f dx dx v dt dy dy Take differentials ' ' ' f zz vx t ' ' ' f dz dz vd x dt dt 2 tt c  2 c dx v dt x ften 2 ' ' f uv u c u 2 ' ' f x f u x dt c  Often written as   1 f vc ' ' ' fx f f u v v v  2 2 1 ' '1 f x u c c 3
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Velocity transformation for y and z ( perpendicular to relative motion) ' ' y dy u d x t  ' ' z dz u d x t 2 ' ' f vd dt c dy    2 ' ' f c z 2 ' ' '1 f dx v ' ' f v 2 '' 1 y c uu 2 2 ' 1 ' c 22 1' yy ff x x vv cc  z z x x u u 4
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Implications of Lorentz Velocity Transformation 0.80 1.00 nenet ' x x f f uv u v  Select u’=(0.2c)i’ + (0.6c)j’ 40 0.60 ty compo n nits of c) 2 ' 1 ' y y x u u u c u y 0.20 0.40 ,y) veloci t (in un 2 1' ' f
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Lecture_35 - PHYS 342 Fall 2011 Lecture 35 Relativistic...

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