midterm_2010 - Physics 523 Midterm Exam Fall 2010 Wednesday...

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Physics 523 Midterm Exam, Fall 2010 Wednesday, May 27, 9:30-10:50am This exam consists of 3 problems (with multiple parts) on 1 page, worth a total of 100 pts. Do all problems, answered in the exam booklet provided, and clearly show all your work. This is a closed-book exam. Non-programmable calculators may be used (though should not be necessary). Remember to write your name in the exam booklet, and write and sign the pledge : I pledge my honor that I have not violated the Honor Code during this examination. Problem 1. [40 pts total] In Minkowski spacetime ds 2 = - dt 2 + dx 2 + dy 2 + dz 2 a curve is parameterized as follows: t ( λ ) = λ ; x ( λ ) = R cos( ωλ ); y ( λ ) = R sin( ωλ ); z ( λ ) = 0 , where R and ω are constants. The following questions all assume the trajectory describes a time-like particle: (a) [10 pts] What is the unit four vector u α ( λ ) tangent to the curve? (b) [5 pts] What restrictions are there on R and ω for the trajectory to be time-like? (c) [10 pts] What is the relationship between the proper time τ of the particle and the parameter λ used to express the curve?
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