Lect08_[Compatibility_Mode]

Lect08_[Compatibility_Mode] - Physics 344 Foundations of...

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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: Chapters 4 and 6 of the text. Notices: If you were unable to attend Tuesday’s help session in room 160, see the grader to pick up and discuss your graded homework.
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Last Lecture and Recitation Recap We are engaged in the derivation of Lorentz transformation equations () xx V t γ = 2 V tt x ⎛⎞ =− ⎜⎟ y y = zz = c ⎝⎠ and their inverse V t = + 2 V x c ′′ =+ y y = = which in a special relativistic Universe relate time and spatial coordinate measurements made in Home and Other frames that are in standard orientation relative to each other. In recitation yesterday we began to consider some of the predictions that special relativity makes as we practiced using these transformation equations. In the third recitation problem we considered a ruler laying on the floor of a train car rolling at constant speed V down a straight section of track. The ruler y makes an angle Φ ’ with the centerline of the car. Most of you made a sketch of the situation like this. φ x
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You focused on the coordinates of the end of the y ruler labeled by the dot and related them to the angle Φ ’. φ x tan / y x ′′ = We were asked to determine the angle Φ that the ruler would make relative to the x axis in the Home frame in which the track is at rest. Many of you initially drew a Home frame picture of the situation like this and y focused your attention on the coordinates of the end of the ruler labeled by the dot Vt G x hat was fine, but it was important to realize this picture is correct at only one That was fine, but it was important to realize this picture is correct at only one time, namely, t = 0 if the Home and Other frames are in standard orientation. Sometime later the ruler would be further along the x axis and the coordinates of that point alone will not determine the angle we were asked for. What we need to know are the locations of the ruler’s ends in the Home frame AT THE SAME TIME. In this regard, measuring the orientation of a moving object is like measuring its length, which we discussed earlier.
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The locations of the ruler’s ends in the Home frame at the same time are y event 2 a pair of events, 1 and 2, with Δ t 21 = 0 sec. φ event 1 he nd oordinate separations between these events are related to the The x and y coordinate separations between these events are related to the angle Φ we want to find, 21 21 tan / y x φ= ΔΔ he Home- ame coordinate separations nd re also related The Home frame coordinate separations Δ t 21 , Δ x 21 and Δ y 21 are also related to the corresponding Other-frame separations Δ t’ 21
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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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Lect08_[Compatibility_Mode] - Physics 344 Foundations of...

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