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Galilean Velocity Transformation Equations |
Consider
a particle in motion with respect to two observers in motion. Let the
observer’s coordinate systems be in standard
configuration so that system S’ moves along the +x-axis of system S
with velocity v. Let the particle’s velocity in system S be 
and in system S’ be 
. Then the classical relationship between the components of
these velocities will be given by
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The
Galilean Velocity Transformation Equations |
Transform |
Inverse
Transform |
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ux,
uy, uz = components of velocity in rest frame S u’x,
u’y, u’z = components of velocity in moving frame S’ v = velocity of S’ along
+x-axis of S |
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These
equations follow immediately from the derivatives of the Galilean
coordinate transformation equations. As usual, the inverse
transformation equations follow from the transformation equations by replacing v
with –v.
Questions:
Q1. An object A is moving to the right with a speed of 0.8 c.
Object B is moving to the left with a speed of 0.8 c. What is the velocity of
object A with respect to object B according to classical physics.
Problems:
P1. Symbol Conversion
Show
that the Galilean velocity equation
given in the previous page for vAC follows immediately from
the first inverse Galilean velocity equation given above for ux through
a simple substitution of appropriate symbols.
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ModPhy1/Unit1/SpecialRelativity/RelativeView/Velocity/