test1 - PHYS5523 Theory of Relativity Test 1 Special...

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Unformatted text preview: PHYS5523 Theory of Relativity Test 1: Special Relativity September 20, 2011 General Instructions: This is a two hour, open book test with three prob- lems. Complete all three problems. Problem 1: Circular Motion and Time Dilation. Consider an object in a circular orbit about a central point, while experi- encing a centripetal acceleration of constant magnitude g . Find u t (the time component of the 4-velocity) for this object, recalling that, in spherical polar coordinates r , θ , φ (with associated unit vectors for these coordinates indicated by hatted quantities) the general expression for 3-acceleration is (with overdots indicating differentiation with respect to time) a = (¨ r- r ˙ φ 2 sin 2 θ- r ˙ θ 2 )ˆ r + ( r ¨ θ + 2˙ r ˙ θ- r ˙ φ 2 sin θ cos θ ) ˆ θ + ( r ¨ φ sin θ + 2˙ r ˙ φ sin θ + 2 r ˙ θ ˙ φ cos θ ) ˆ φ (1) Thus show how the ratio of the proper time for this object compares to the proper time of a clock at the center of the rotation....
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test1 - PHYS5523 Theory of Relativity Test 1 Special...

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