Chapter 1 Learning ObjectivesConcepts and Skills to Review
algebra, geometry, and trigonometry (Appendix A)
Summary
Terms used in physics must be precisely defined. The same term may have a different meaning in physics from the meaning of the same word in other contexts.
A working knowledge of algebra, geometry, and trigonometry is essential in the study of physics.
The factor by which is quantity is increased or decreased is the ratio of the new value to the original value.
When we say that A is proportional to B (written A∝B), we mean that if B increases by some factor, then A must increase by the same factor.
In scientific notation, a number is written as the product of a number between 1 and 10 and a whole number power of ten.
Significant figures are the basic grammar of precision. They allow us to communicate quantitative information and indicate the precision to which that information is known.
When two or more quantities are added or subtracted, the result is as precise as the least precise of the quantities. When quantities are multiplied or divided, the result has the same number of significant figures as the quantity with the smallest number of significant figures.
Order of magnitude estimates and calculations are made to be sure the more precise calculations are realistic.
The units used for scientific work are those from the Système International (SI). SI uses seven base units, which include the meter (m), the kilogram (kg), and the second (s) for length, mass, and time respectively. Using combinations of the base units, we can construct other derived units.
If the statement of a problem includes a mixture of different units, the units should be converted to a single, consistent set before the problem is solved. Usually the best way is to convert everything to SI units.
Dimensional analysis is used as a quick check on the validity of equations. Whenever quantities are added, subtracted, or equated, they must have the same dimensions (although they may not necessarily be given in the same units).
Mathematical approximations aid in simplifying complicated problems.
Problem-solving techniques are skills that must be practiced to be learned.
A graph is plotted to give a picture of the data and to show how one variable changes with respect to another. Graphs are used to help us see a pattern in the relationship between two variables.
Whenever possible, a careful choice is made of the variables plotted so that the graph displays a linear relationship.
