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

2. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 1.2: Solving problems in physics Identify, set up, execute, evaluate

3. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 1.3-1.4: Units, Consistency, and Conversions Base units are set for length (m), time (s), and mass (kg). An equation must be dimensionally consistent (be sure you’re “adding apples to apples”). “Have no naked numbers” (always use units in calculations). Examples 1.1 and 1.2

4. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 1.5: Uncertainty and significant figures Operations on data must preserve the data’s accuracy. –Accuracy is indicated by the number of significant figures or by a stated uncertainty. For multiplication and division, round to the smallest number of significant figures. For addition and subtraction, round to the least accurate data. Always use scientific notation when it’s appropriate.

5. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 1.6: 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.

6. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Scalars vs. Vectors Scalar quantities are numbers and combine with the regular rules of arithmetic. Vector quantities have direction as well as magnitude and combine according to the rules of vector addition. –The negative of a vector has the same magnitude but points in the opposite direction. –It doesn’t matter where a vector is located -- only the magnitude and direction matter.

7. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 1.7: Vectors Vectors show magnitude and displacement, drawn as a ray.

8. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 1.7: Vector Addition Vectors may be added graphically, “head to tail.”

9. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 1.7: Vector Addition

10. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 1.7:Vector addition Refer to Example 1.5.

11. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 1.8: Components of Vectors 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 measured from the +x axis).

12. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 1.8: Components of vectors

13. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 1.8: Components of Vectors Refer to Example 1.6.

14. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Finding a Vector’s Magnitude and Direction A = √(A x 2 + A y 2 ) tanθ = A y /A x

15. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 1.8: Calculations using components A = √(A x 2 + A y 2 ) tanθ = A y /A x

16. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 1.8: Calculations using components Refer to Example 1.7

17. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 1.9: Unit vectors 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.

18. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 1.10: Multiplying Vectors - The scalar product Termed the “dot product.” The result is a scalar quantity If you know the magnitude and direction of the vectors: AB = ABcosφ If you know the components of the vectors: AB = AxBx + AyBy + AzBz

19. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 1.10: Multiplying Vectors - The vector product Termed the “cross product.” The result is a vector quantity A × B = ABsinφ This is the magnitude of the solution. Use the Right-Hand Rule to determine the direction. A × B = (AyBz – AzBy)i + (AzBx – AxBz)j + (AxBy – AyBx)k