Fundamentals of Mechanics/Units and Vectors/Dimensional Analysis

Conversion Factors Vectors The symbols used to specify the dimensions of length, mass, and time are L length, M mass, and T time, respectively. Dimensional analysis is a method used to check the validity of an equation and to derive correct expressions. Only the same dimensions can be added or subtracted; that is, they obey the rules of algebra. To check the validity of an equation, the terms on both sides must have the same dimensions. The dimensions of a physical quantity are denoted using square brackets [ ]. For example, the dimensions of the volume are , and those of acceleration are . 1.3 Show that the expression is dimensionally consistent, where v represents the speed, x represents the displacement, and a represents the acceleration of the object. Each term in the equation has the same dimensions, and therefore it is dimensionally correct.