Chapter1_3

# Chapter1_3 - v V v V dt dx dt dt V dt dx dt dx v ′ = = =...

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PHY3063 R. D. Field Department of Physics Chapter1_3.doc University of Florida Galilean Transformation Consider two frames of reference the O-frame (label events according to t,x,y,z) and the O'-frame (label events according to t',x',y',z') moving at a constant velocity V, with respect to each other at let the origins coincide at t= t' = 0. In the Galilean transformations the O and O' frames are related as follows: z z y y t V x x t t = = + = = z z y y Vt x x t t = = = = Velocity Transformation: z z y y x x v dt dz dt dz dt dz v v dt dy dt dy dt dy
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Unformatted text preview: v V v V dt dx dt dt V dt dx dt dx v ′ = = = = ′ = = = = + ′ = + = + = = ' ' ' ' ' ' ' ' ' ' Acceleration Transformation: z z y y x x a dt z d dt z d dt z d a a dt y d dt y d dt y d a a dt x d dt x d dt x d a ′ = = = = ′ = = = = ′ = = = = 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ' ' ' ' ' ' ' ' ' y x z y' z' x' V Event O: (t,x,y,z) O': (t'.x',y',z') O O' x' x Vt' Time is absolute! Classical velocity addition formula! Acceleration is a Galilean invariant!...
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