Galilean Transformation


Motion is a relative concept . You are sitting on a train. A object on trains seems to be at rest from your perspective but it is in motion from the person standing on the ground.So it is tied to particular frame of refrence choosen by observer.
Now Different observer may use different frame of refrence , And velocity ,acceleration may be different from these different frame of refrence
It is important to know how these measurement in different frame of refrence are related.
For two observer S1 and S2 who move relative to each other with rectilinear motion, The velocity,displacement and acceleration of an object measured from these two observer are related as
r2=r1 -R
Where r1 is the position vector of object from observer S1 and r2 is the position vector of object from observer S2. R is the position of observer S2 from S1
v2=v1 -v
Where v1 is the velocity of object relative to observer S1 and v2 is the velocity of object relative to observer S2. v is the velocity S2 relative to S1
a2=a1 -a
Where a1 is the acceleration of object relative to observer S1 and a2 is the acceleration of object relative to observer S2. a is the acceleration S2relative to S1
When the two observer are moving in uniform relative translation motion with velocity v and t=0 when the observer were coincident,these equation becomes
r2=r1 -vt
v2=v1 -v
a2=a1
t1=t2
The above equation are called Galilean transformation of coordinates ,velocities and accelerations
So acceleration of the object remains same for all observer in uniform relative translational motion

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