Physics 523 Midterm Exam, Fall 2010Wednesday, May 27, 9:30-10:50amThis exam consists of 3 problems (with multiple parts) on 1 page, worth a total of 100 pts. Doallproblems, answered in the exam booklet provided, and clearly show all your work. This is aclosed-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 myhonor that I have not violated the Honor Code during this examination.Problem 1. [40 pts total]In Minkowski spacetimeds2=-dt2+dx2+dy2+dz2a curve is parameterized as follows:t(λ) =λ;x(λ) =Rcos(ωλ);y(λ) =Rsin(ωλ);z(λ) = 0,whereRandωare constants. The following questions all assume the trajectory describes atime-likeparticle:(a) [10 pts]What is theunitfour vectoruα(λ) tangent to the curve?(b) [5 pts]What restrictions are there onRandωfor the trajectory to be time-like?(c) [10 pts]What is the relationship between theproper timeτof the particle and the parameterλused to express the curve?
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