Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley PowerPoint ® Lectures for University Physics, Twelfth Edition – Hugh D. Young and Roger A. Freedman Chapter 1 Units, Physical Quantities, and Vectors

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Goals for Chapter 1 To prepare presentation of physical quantities using accepted standards for units To understand how to list and calculate data with the correct number of significant figures To manipulate vector components and add vectors To prepare vectors using unit vector notation To use and understand scalar products To use and understand vector products

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Introduction The study of physics is important because physics is one of the most fundamental sciences, and one of the first applications of the pure study, mathematics, to practical situations. Physics is ubiquitous, appearing throughout our “day-to-day” experiences.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Solving problems in physics Identify, set up, execute, evaluate

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Standards and units Base units are set for length, time, and mass. Unit prefixes size the unit to fit the situation.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Unit consistency and conversions An equation must be dimensionally consistent (be sure you’re “adding apples to apples”). “Have no naked numbers” (always use units in calculations). Refer to Example 1.1 (page 7) and Problem 1.2 (page 8).

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Uncertainty and significant figures—Figure 1.7 Operations on data must preserve the data’s accuracy. For multiplication and division, round to the smallest number of significant figures. For addition and subtraction, round to the least accurate data. Refer to Table 1.1, Figure 1.8, and Example 1.3. Errors can result in your rails ending in the wrong place.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Estimates and orders of magnitude Estimation of an answer is often done by rounding any data used in a calculation. Comparison of an estimate to an actual calculation can “head off” errors in final results. Refer to Example 1.4.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Vectors—Figures 1.9–1.10 Vectors show magnitude and displacement, drawn as a ray.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Vector addition—Figures 1.11–1.12 Vectors may be added graphically, “head to tail.”

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Vector additional II—Figure 1.13

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Vector addition III—Figure 1.16 Refer to Example 1.5.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Components of vectors—Figure 1.17 Manipulating vectors graphically is insightful but difficult when striving for numeric accuracy. Vector components provide a numeric method of representation. Any vector is built from an x component and a y component. Any vector may be “decomposed” into its x component using V*cos θ and its y component using V*sin θ (where θ is the angle the vector V sweeps out from 0°).

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Components of vectors II—Figure 1.18

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Finding components—Figure 1.19 Refer to worked Example 1.6.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Calculations using components—Figures 1.20–1.21 To find the components, follow the steps on pages 17 and 18. Refer to Problem-Solving Strategy 1.3.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Calculations using components II—Figure 1.22 See worked examples 1.7 and 1.8.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Unit vectors—Figures 1.23–1.24 Assume vectors of magnitude 1 with no units exist in each of the three standard dimensions. The x direction is termed I, the y direction is termed j, and the z direction, k. A vector is subsequently described by a scalar times each component. A = A x i + A y j + A z k Refer to Example 1.9.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley The scalar product—Figures 1.25–1.26 Termed the “dot product.” Figures 1.25 and 1.26 illustrate the scalar product.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley The scalar product II—Figures 1.27–1.28 Refer to Examples 1.10 and 1.11.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley The vector product—Figures 1.29–1.30 Termed the “cross product.” Figures 1.29 and 1.30 illustrate the vector cross product.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley The vector product II—Figure 1.32 Refer to Example 1.12.