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Unformatted text preview: PHYS126 Supplementary Notes 3 In recent lectures, we have learnt several concepts of special relativity. In this note, several exercises of each topic are shown. 1. Lorentz transformation Now, define two inertial frames S and S’. Frame S’ moves in the +x direction with the speed v relative to the frame S. For the same event: ( , , , ) x y z t in {S} and ( , , , ) x y z t ′ ′ ′ ′ in {S’}. Galilean Transformation Lorentz Transformation x x vt ′ = ( ) x x vt γ ′ = 1 < = c v β y y ′ = y y ′ = 1 1 1 2 = β γ z z ′ = z z ′ = t t ′ = 2 vx t t c γ ′ = The Lorentz Transformation leads to: H1HTime Dilation H2HLength Contraction H3HLoss of Simultaneity (‘Time’ as universal quantity) Exercise: The frame s and s ′ are in the standard configuration with relative velocity 0.8c along Ox . (a)What are the coordinates ( 29 1 1 1 1 , , , x y z t in s of an event that occurs on the x ′ axis with 1 1 1500 , 5 x m t s μ ′ ′ = = ? (b)Answer the same for a second event on the x ′ axis with 2 2 1500 , 10 x m t s μ ′ ′ =  = ....
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 Spring '11
 HoBunCHAN
 Physics, Inertia, Special Relativity, Lorentz Transformation

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