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motion: TOC for Knowledge Concepts, Exercises, and Solutions

The following mathematical expressions summarize the basics of special relativity:

  l' = l * sqrt(1 - (v/c)^2)    (length contraction)

  t' = t / sqrt(1 - (v/c)^2)    (time dilation)

  m' = m / sqrt(1 - (v/c)^2)    (mass increase)

The quantity sqrt(1 - (v/c)^2), where v is the velocity of an object and c is
the speed of light, is known as the Lorentz factor.  (Sometimes the term 
refers to the reciprocal of that expression - be careful.) The Lorentz factor, 
named after the Nobel Prize-winning Dutch physicist who articulated it,
is always less than or equal to one, and approaches zero as v increases.

The variables l, l', t, t', m, and m' are confusing as well; so be sure to 
remember that if you are moving, distances grow shorter, time runs slower, and 
mass goes up - hence the terms "length contraction," "time dilation," and "mass 
increase." If you are moving, you will experience less time than a non-moving 
observer who's watching you. Also, if you are moving, you will see shorter 
distances than a non-moving observer looking at the same spot.  And if you are 
moving, a non-moving observer will see your mass get larger.

Remember that the speed of light is given by c = 2.997 * 10^8 m/sec.  This is
equivalent to 186,282 miles per second, or about 5.8 trillion miles per year.