Lect06_[Compatibility_Mode]

Lect06_[Compatibility_Mode] - Physics 344 Foundations of...

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Physics 344 Foundations of 21 st Century Physics: Relativity, Quantum Mechanics and Their Applications Their 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 appointment We 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 ˆ y ˆ y transformations between inertial coordinate systems. The figure shows the unit vectors pointing in the direction of the x and y axes of one ˆ sin( ) x θ θ ˆ x 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. 1 ˆ 1 ˆ cos( ) y θ θ ˆ x Since the unit vectors of the primed system ˆ cos( ) x θ sin( ) y θ ˆ ˆ ˆ cos( ) sin( ) x x y θ θ = + 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. ˆ ˆ ˆ sin( ) cos( ) y x y θ θ = − + ˆ ˆ z z = Knowing the relationship between the sets of unit (basis) vectors allows us to transform the coordinates of any vector! ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ (cos( ) sin( ) ) '( sin( ) cos( ) ) ' ˆ ˆ ˆ ˆ ˆ ˆ ( cos( ) sin( )) ( 'sin( ) cos( )) ' r x x y y z z x x y y x y z z x y x x y y z z xx yy zz θ θ θ θ θ θ θ θ ′ ′ ′ ′ ′ ′ = + + = + + + + + + + + + G = From this we simply read off the transformation equations. cos( ) sin( ) 'sin( ) cos( ) ' x x y y x y z z θ θ θ θ = = + =
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