Talha's Physics Academy
Galilean Transformation Equations
Video Lecture: Galilean Transformation Equations
Watch the complete video lecture explaining the derivation and concepts of Galilean transformation equations:
Galilean Transformation Equations
The Galilean transformation equations describe the relationship between the coordinates of an event in two different inertial frames of references. These equations were formulated by Galileo and are applicable when the relative velocities involved are much smaller than the speed of light ($v \ll c$).
Derivation and Setup
Let $S$ and $S'$ (referred to as $x$ and $x'$ frames) be two inertial frames. Let frame $S$ be at rest and frame $S'$ move with uniform velocity $v$ along the positive X-direction. We assume that $v \ll c$. Let the origins of the two frames coincide at $t = 0$.
Suppose some event occurs at the point $P$.
- The observer $O$ in frame $S$ determines the position of the event by the coordinates $(x, y, z)$.
- The observer $O'$ in frame $S'$ determines the position of the event by the coordinates $(x', y', z')$.
- Let the time elapse at the same rate in both frames, i.e., $t = t'$.
There is no relative motion between the frames along the axes of Y and Z, so $y = y'$ and $z = z'$. Measurements in the X-direction made in the stationary frame will be greater than those made in the moving frame by the amount $vt$, which is the distance $S'$ has moved in the X-direction.
Transformation Equations
$y' = y$
$z' = z$
$t' = t$
Alternatively, expressing unprimed coordinates in terms of primed coordinates:
$y = y'$
$z = z'$
$t = t'$
This set of equations is known as the Galilean transformation equations.
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