Physics 344Foundations of 21stCentury Physics: Relativity, Quantum Mechanics and Their ApplicationsTheir Applications Instructor: Dr. Mark Haugan Office: PHYS 282[email protected]TA: Dan Hartzler Office: PHYS 7[email protected]Grader: Shuo Liu Office: PHYS 283[email protected]Office Hours: If you have questions, just email us to make an appointmentWe enjoy talking about physics!appointment. Reading: Chapter 3 of the text. Notices: Graded homework will be returned on Tuesdays during the help session in PHYS 160 from 1:30 to 3:30.
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Recitation Recap A way to use vectors to understand and work with ˆyˆy′transformations between inertial coordinate systems.The figure shows the unit vectors pointing in the direction of thexandyaxes of oneˆsin( )xθ−θˆx′in the direction of the and axes of one coordinate system and the x’ and y’ axes of another one rotated relative to the first one about their common z, z’axis. 1ˆ1ˆcos( )yθθˆxSince the unit vectors of the primed systemˆcos( )xθsin( )yθˆˆˆcos( )sin( )xxyθθ′=+Since the unit vectors of the primed system are vectors, we can represent them as a sum of vectors in the directions of the unprimed unit vectors. ˆˆˆsin( )cos( )yxyθθ′= −+ˆˆzz′=Knowing the relationship between the sets of unit (basis) vectors allows us to transform the coordinates of any vector! ˆˆˆˆˆˆˆˆ(cos( )sin( ) )'(sin( )cos( ) )'ˆˆˆˆˆˆ(cos( )sin( ))( 'sin( )cos( ))'rx xy yz zxxyyxyz zxyxxyyz zxxyyzzθθθθθθθθ′ ′′ ′′ ′′=++=++−++′′′+++≡++G=−From this we simply read off the transformation equations. cos( )sin( ) 'sin( )cos( ) 'xxyyxyzzθθθθ′′′=−=+=