Lect06_[Compatibility_Mode]

Lect06_[Compatibility_Mode] - Physics 344 Foundations of 21...

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Unformatted text preview: Physics 344 Foundations of 21 st Century Physics: Relativity, Quantum Mechanics and heir 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 ppointment e enjoy talking about physics! appointment. We enjoy talking about physics! 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. 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 the direction of the nd xes of one ˆ sin( ) x θ − θ ˆ x ′ in the direction of the x and y 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 1 ˆ cos( ) y θ θ ˆ x ince the unit vectors of the primed system ˆ cos( ) x θ ˆ 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 y x x y y z z x x y y z z θ θ θ θ ′ ′ ′ ′ ′ ′ ′ = + + = + + − + + ′ ′ ′ + + + ≡ + + G ( cos( ) sin( )) ( 'sin( ) cos( )) ' x y x x y y z z x x y y z z θ θ θ θ = − + + + ≡ + + 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 ′ ′ ′ = − = + = One final point about our vector notations: We write ˆ ˆ ˆ r x x y y z z = + + G x ⎡ ⎤ instead of or , , r x y z G ¡ r y z ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ G ¡ make explicit which unit (basis) vectors we are using We to make explicit which unit (basis) vectors we are using. We need to be very clear about this when we are working with more than one coordinate system at a time. than one coordinate system at a time....
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This note was uploaded on 11/26/2010 for the course PHYS 344 taught by Professor Garfinkel during the Spring '08 term at Purdue.

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Lect06_[Compatibility_Mode] - Physics 344 Foundations of 21...

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