Dimensional Analysis is an extremely important tool for the physicist. The basic principle behind this is that if you have an equation the dimensions of the physical quantity on the right should be the same as the dimensions of the physical quantity on the left.
Consider the equation
x = vt
The dimensions of x(position
) are L. (L stands for length). The dimensions of v(velocity
) are LT-1
where T stands for Time
. The dimensions of T(time) are just T. So the dimensions of the RHS are LT-1
* T = L.
Thus the dimensions of the two sides match and the equation is dimensionally consistent
This is an important tool in situations which are difficult to analyze using other means. Let us say u want to find a relation for one quantity in terms of other quantities and the relation is difficult to derive analytically. So u can just find a combination of the other quantities which has the right dimension. Of course this would only generally give the correct order of magnitude but that is Okay for an estimate.