Frame Of Reference

                               

                          -When  all the distance of a particle  (along X-axis,Y-axis and Z-axis) from the origin of any frame  and time is measured then the frame(we have done all the measurement with respect to it) is called "FRAME OF REFERENCE".

         Here ,Frame of reference divided in two types (on the basis of VELOCITY)-

• INERTIAL FRAME OF REFERENCE 
• NON-INERTIAL FRAME OF REFERENCE

             

• INERTIAL FRAME OF REFERENCE :-

                                                                        
  When a frame of reference moves with a constant velocity OR remains at rest ,called an Inertial Frame of Reference.

      

• NON-INERTIAL FRAME OF REFERENCE:-

                                                                                       When a frame of reference moves with an acceleration (i.e.variable velocity ) is called a Non-inertial Frame of Reference.

               

                                                 

GALILEAN TRANSFORMATIONS

                 

                        Let's start to know about Galilean Transformations -

                                Suppose we (Observer A) are standing and watching an event at time t=0 and another man (Observer B) is also watching this same event,like this-

     

           

  

                   when we and another observer were watching this event ,were in one frame of reference(i.e.  the event was at equal  distance from observer A and  B at time t=0)

   After time t ,Observer B moves towards to  the event with velocity u,

                       Now ,here will be two frame of reference (xyz - frame of reference and x'y'z'-frame of reference ),One with respect to Observer A and second with respect to observer B  because observer B has  changed  his distance from the event .

 

                      If you find the relation between observer A and B-

                  Measured length along x-axis to the event = (ut +x')

                                                           x=ut+x'    ;                             .

               and so on,                           y=y'          ;

                                                           z=z'          ;

                                                           t=t'( because the event is happening at the same time for both observer)

    

                                Or                   x'=x-ut

                                                        y'=y

                                                        z'=z

                                                        t'=t

These Equations are called Galilean Transformation equations.

                            differentiating with respect to x of these equations-

                                     dx'/dt=dx/dt-udt/dt     {u=constant velocity}

or                          vx'=vx-u

and                        vy'=vy
                               vz'=vz
 and again    differentiating
                           ax'=ax    {u=constant
                                           ay'=ay
                                           az'=az

                  Galilean Invariance

                   you can write a=ax+ay+az

                                                           

                               Force-

                                         F=ma

                                           F'=ma'(because a=a')

                  So             

                                        F=F'