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HW-571-1 - 2 and simplify this expression in two relevant...

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1 Phys 571 , Fall 2010 Assignment #1 Due: 8/30/2010 1. Show explicitly that two successive Lorentz transformations in the same direction are equiv- alent to a single Lorentz transformation with a velocity v = v 1 + v 2 1 + ( v 1 v 2 /c 2 ) . 2. Two rods of proper length l 0 move towards each other with the same velocity v with respect to a certain reference frame. What is length l of each rod as seen in the other rod frame? Hint: one of many ways to solve this problem is to use the boost-invariance of ( u μ 1 + u μ
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Unformatted text preview: ) 2 and simplify this expression in two relevant reference frames. 3. Given frame K moving with an arbitrary velocity V with respect to frame K (not necessarily parallel to the x-axes). (a) Find formulas for Lorentz transformations from K to K in vector form. Hint: decompose r as r = r k + r ⊥ where r ⊥ and r k are perpendicular and parallel components with respect to V . (b) Derive the velocity addition formula in vector form....
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