Dimensional Reasoning

Abstract

1. How dimensions, units, and magnitudes characterize physical variables/measurement. 2. That a limited number of primitive dimensions can be arranged to characterize all physical phenomena 3. Dimensions are intrinsic to the variables themselves; units are not 4. Measurement and quantification of variables depend on units which are established by convention, e.g., SI 5. Rudiments of the SI and English measurement systems 6. Why we still use more than one system of units 7. Dimensions, units, and quantities may be manipulated algebraically 8. All terms in an equation must have identical primitive dimensions to be consistent 9. Many physical phenomena can be expressed in terms of its contributing parameters as a single term 10. Dimensional reasoning can be used to infer the relationship between those parameters 11. What are “dimensionless” variables 12. Why physical phenomena are sometimes expressed in terms of dimensionless variables 13. Descriptions of and differences between geometric, kinematic, and dynamic similarity 14. Why old movies look “strange” when movie-makers use models to simulate disasters 15. When scale models can be used to predict full-size phenomena. When they can’t.