Thursday, 29 November 2012

Length Contraction, Length Contraction in Relativity, What is Length Contraction?


When a body moves with very high speed v relative to an observer then it appears to be contracted by a factor in the direction of motion only. This concept is known as length contraction and this shows clearly that length is not absolute but relative.

Let us consider two inertial frame s and s’. s’ is moving with velocity v relative to s along +x direction. Frame s is at rest. Let a rod AB is laying along the x axis in frame s. If x1 and x2 be coordinate of ends A and B respectively then the length L0 of the rod in frame s is given by 

 Let an observer in s’ measure the length of the same rod and its x1’ and x2’ are the coordinate of end A and B of the rod at the same time then the length of the rod L will be given by

According to Inverse Lorentz Transformation we have

Hence the length of rod moving with velocity v relative to the observer is contracted by a factor  in the direction of motion. This phenomenon is also called Lorentz-Fitzgerald Contraction.

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