Dimensional analysis of models and data sets

Dimensional analysis is a widely applicable and sometimes very powerful technique that is demonstrated here in a study of the simple, viscous pendulum. The first and crucial step of dimensional analysis is to define a suitably idealized representation of a phenomenon by listing the relevant variables, called the physical model. The second step is to learn the consequences of the physical model and the general principle that complete equations are independent of the choice of units. The calculation that follows yields a basis set of nondimensional variables. The final step is to interpret the nondimensional basis set in the light of observations or existing theory, and if necessary to modify the basis set to maximize its utility. One strategy is to nondimensionalize the dependent variable by a scaling estimate. The remaining nondimensional variables can then be formed in ways that define aspect ratios or that correspond to the ratio of terms in a governing equation. (C) 2003 American Association of Physics Teachers.