Cap 01 LectureOutline

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

PowerPoint® Lectures forUniversity Physics, Twelfth Edition – Hugh D. Young and Roger A. Freedman

Lectures by James Pazun

Chapter 1

Units, Physical Quantities, and Vectors


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


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.


Solving problems in physics

• Identify, set up, execute, evaluate


Standards and units

• Base units are set for length, time, and mass.

• Unit prefixes size the unit to fit the situation.


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).


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.


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.


Vectors—Figures 1.9–1.10

• Vectors show magnitude and displacement, drawn as a ray.


Vector addition—Figures 1.11–1.12

• Vectors may be added graphically, “head to tail.”


Vector additional II—Figure 1.13


Vector addition III—Figure 1.16



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°).


Components of vectors II—Figure 1.18


Finding components—Figure 1.19

• Refer to worked Example 1.6.


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.


Calculations using components II—Figure 1.22

• See worked examples 1.7 and 1.8.


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 = Axi + Ayj + Azk



The scalar product—Figures 1.25–1.26

• Termed the “dot product.”

• Figures 1.25 and 1.26 illustrate the scalar product.


The scalar product II—Figures 1.27–1.28

• Refer to Examples 1.10 and 1.11.


The vector product—Figures 1.29–1.30

• Termed the “cross product.”

• Figures 1.29 and 1.30 illustrate the vector cross product.


The vector product II—Figure 1.32


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