5 Dimensional Analysis The dimensions of a physical quantity indicate how it is related to the fundamental quantities length L, mass M, time T and current I. In every equation in physics the dimensions must be consistent in every term in the equation. The dimension of distance is length (L), the dimension of mass is mass (M), and the dimension of time is time (T). For example, consider the equation Distance = speed ×time (1) The dimension of distance is length (L), the dimension of speed is length per time (L/T), and the dimension of time is time (T). Examining the dimensions of each side of the equation shows L = L T ×T (2) Time cancels out on the right side, so both sides of the equation have the dimension of length. This illustrates the fact that the units of each variable in an equation are to be included in the calculation. They are multiplied and divided as though they are algebraic quantities. It is helpful to check the units for each term in an equation, since any inconsistency indicates an error has been made, and you are thereby alerted to search for it. Note that the dimension of force is ML/T2, and for acceleration it is L/T2. 3
