Homework_07

Homework_07 - PHYS342 FallSemester2011 HomeworkNo.7...

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1 PHYS 342 Fall Semester 2011 Homework No. 7 Due: December 7, 2011 1. A reoccurring theme in the physics of relativity is the transformation of results between different co-ordinate systems. One important non-relativistic transformation involves two coordinate systems that are rotated one with respect to the other. Suppose there are two co- ordinate systems (x,y,z) and (x’,y’,z’) as shown to the right. The primed co-ordinate system is rotated through an angle + as shown. The co- ordinates of a point P (x,y,z) are related to the co-ordinates of the same point P (x’,y’,z’) when measured in the rotated co-ordinate system by a) Suppose there are two vectors ˆˆ ˆ ˆ 61 0 9 3 3 A ij k a n d B i j k   in the unprimed co-ordinate system. What are these vectors when measured in the primed co-ordinate system if the rotation angle =35 o ? b) Evaluate the vector products ABandA B   in both the primed and unprimed co- ordinate systems? Are either of these two vector operations invariant under coordinate transformation? P x x’ y y’ z z’ 'c o s s i n 0 's i n c o s 0 '0 0 1 x x y y zz        
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2 c) What is the length of the vector ( A A  ) in both the primed and unprimed co- ordinate systems. Is the length of a vector invariant under rotation of the co-ordinate axes? 2. A spacecraft travels in a straight line at a speed of 0.50c. An astronaut holds a meter stick parallel to the direction of travel.
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Homework_07 - PHYS342 FallSemester2011 HomeworkNo.7...

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