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# Unit 8 - Physics 225 Relativity and Math Applications...

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Physics 225 Relativity and Math Applications Spring 2010 Unit 8 Review of Special Relativity N.C.R. Makins S.A. Lamb University of Illinois at Urbana-Champaign © 2010

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Physics 225 8.2 Unit 8: SR in a nutshell The midterm is next week on Tuesday, and it will mark the end of our study of special relativity. What a perfect opportunity for a review! First, here are all the key formulas neatly summarized on one page. No explanations are given: understanding the formulas is your part. p = E / c for a light ray (photon) I = ( c ! t ) 2 " ( ! x ) 2 " ( ! y ) 2 " ( ! z ) 2 ! F = d ! p dt ! p = m ! v W = ! F i d ! l = ! E " E = mc 2 = ( pc ) 2 + ( m 0 c 2 ) 2 KE = E ! m 0 c 2 m = ! m 0 ! p = ! m 0 ! v E = ! m 0 c 2 ! = pc E ! = E m 0 c 2 where ! = v / c and ! = 1/ 1 " ( v / c ) 2 as always. ! μ " # \$ % \$& 0 0 % \$& \$ 0 0 0 0 1 0 0 0 0 1 ( ) ) ) ) * + , , , , x μ ! ( ct , x , y , z ) d ! = dt " u ! u = 1 1 " ( u / c ) 2 ! μ " dx μ d # = \$ u c , u x , u y , u z ( ) p μ ! m 0 " μ = E c , p x , p y , p z # \$ % & ( f ' f = 1 ! " 1 + " E ! = hf u x ' = u x ! v 1 ! u x v / c 2 u y ' = u y / ! 1 " u x v / c 2 u z ' = u z / ! 1 " u x v / c 2 t = γ ( t β x / c ) x = γ ( x β t c ) y = y z = z t = γ ( t + β x / c ) x = γ ( x + β t c ) y = y z = z ! u = d ! r dt = dx dt , dy dt , dz dt ! " # \$ % &
Physics 225 8.3 Exercise 8.1: Astronaut and radio signals An astronaut takes off in a rocket at t = 0, traveling at v = β c relative to the Earth. She sends a greeting back to her family on Earth by radio at intervals of time T, starting at time T after the launch, according to the clock on her rocket. a) What are the times that her family receives the radio messages back on Earth, using clocks stationary on the Earth? (Give your answers in terms of T, β , and c, as needed.) b) The astronaut would like her family to receive the messages at a radio frequency of f 0 . At what frequency should she transmit her messages?

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Physics 225 8.4 Exercise 8.2: Borg Ship 199HM Final Exam problem 1 The villainous Borg travel through interstellar space in a giant cubic ship. Borg technicians on board the ship carefully measure the ship’s dimensions: it is a perfect cube with sides of length 2 L .
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Unit 8 - Physics 225 Relativity and Math Applications...

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