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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
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
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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.
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Solving problems in physics
• Identify, set up, execute, evaluate
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Standards and units
• Base units are set for length, time, and mass.
• Unit prefixes size the unit to fit the situation.
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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).
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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.
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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.
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Vectors—Figures 1.9–1.10
• Vectors show magnitude and displacement, drawn as a ray.
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Vector addition—Figures 1.11–1.12
• Vectors may be added graphically, “head to tail.”
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Vector additional II—Figure 1.13
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Vector addition III—Figure 1.16
• Refer to Example 1.5.
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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°).
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Components of vectors II—Figure 1.18
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Finding components—Figure 1.19
• Refer to worked Example 1.6.
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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.
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Calculations using components II—Figure 1.22
• See worked examples 1.7 and 1.8.
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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
• Refer to Example 1.9.
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The scalar product—Figures 1.25–1.26
• Termed the “dot product.”
• Figures 1.25 and 1.26 illustrate the scalar product.
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The scalar product II—Figures 1.27–1.28
• Refer to Examples 1.10 and 1.11.
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The vector product—Figures 1.29–1.30
• Termed the “cross product.”
• Figures 1.29 and 1.30 illustrate the vector cross product.