Importance of Frame of Reference:

The importance of each term is as described below.

(i) v   = d r_A / dt = d X _A / dt  I¯ +  d Y_A / dt J¯

This is the absolute velocity of point A in the vehicle and as we have supposed A as a pole, it also represents the translatory velocity of the vehicle.

(ii)   v _AB  = ω × ( x_B i + y_B  j) = ω × r_AB

This represents the rotation of point B with respect to pole A which is attained by treating vector r_AB of constant magnitude of the vehicle itself.

 (iii)

It is the velocity of B with respect to reference axes x, y associated to the vehicle. Therefore It is the velocity of B relative to the vehicle or called the relative velocity of B and represented as.

Further we may combine

Where we may call v b is the velocity of the particle B if it was associated to the vehicle and this is termed as vehicle or base velocity.

or

Therefore we can say relative velocity is the difference of absolute and vehicle velocity.