Dimensional formulae and dimensional equations
In physics quantity describe of dimension as the power in which the fundamental quantities are raised to express the physical quantity .in this we will showing the dimension of mass ,length ,and time are described as {M},{L} and {T} respectively
Example :
Velocity =displacement/Time : L/T = LT-1 = MoLT-1 when there is no mass, Mo = 1 (algebraic theory of indices).
According to above example we can say that the dimension of velocity are, zero in mass, 1 in length and -1 in time.
Formula of Dimensional
The formula of dimensional is defined as the expression of the physical quantity in term of it's basic unit with exact dimension. so dimension force is F = MLT-1
unit of force kg*m/s2
Dimension equation and its principal
Any equation which contains physical quantities with dimensional formula is known as dimensional equation. Dimensional equation is obtained by equating dimensional formula on right hand side and left hand side of an equation .and the dimensions of fundamental quantities on left hand side of an equation must be equal to the dimensions of the fundamental quantities on the right hand side of that equation. suppose three quantities i have like X, Y and Z so Z = X + Y. according to this principle, the dimensions of Z are equal to the dimensions of X and Y.
Dimensional equation of v=u+ at is :
Mo LT-1 = MoLT-1 X M0L0LT-1
Uses and Limitations of Dynamic Equation and Analysis :
it is used to convert value of physical quantity from one system of unit to another system and to fine the dimension of the constant in the given relation and it derived the relation between various physical quantities.
It does not give information about the dimensional constant, and if a quantity depends on more than three factors having dimension, the formula cannot be derived also cannot derived the formulae containing trigonometric function , exponential functions, logarithmic function. The accurate form of relation cannot be developed when there is more than one part in any relation.