SKEDSOFT

Physics For Engineers - 1

The Relativistic Addition of Velocity: In classical physics, if we consider a case of a train moving with velocity with respect to ground and a passenger on the train moving with a velocity with respect to train, Then the velocity of passanger with respect to the ground is,

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This is simply Galilean or classical velocity addition theorem. Let us discuss how the velocities are added according to special theory of relativity.

Consider for a special case, all velocities are along x -direction of two inertial frames and is the laboratory frame and - is moving frame with constant velocity . A body moves in frame with a velocity and its position can be written as . The speed of the body with respect to frame can be calculated as follows,    
                       

          
where
= x / t is the velocity of body with respect to frame. This is the relativistic or Einstien velocity addition theorem.

If and are small compared to which is the classical result. On the other hand, if would also be equal to irrespective of the value of .

 

Hence, when