1 / 19

Chapter 1

Chapter 1. Units, Physical Quantities, and Vectors. 1.2: Solving problems in physics. Identify, set up, execute, evaluate. 1.3-1.4: Units, Consistency, and Conversions. Base units are set for length (m), time (s), and mass (kg).

tammy
Download Presentation

Chapter 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 1 Units, Physical Quantities, and Vectors

  2. 1.2: Solving problems in physics • Identify, set up, execute, evaluate

  3. 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. 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. 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. 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. 1.7: Vectors • Vectors show magnitude and displacement, drawn as a ray.

  8. 1.7: Vector Addition • Vectors may be added graphically, “head to tail.”

  9. 1.7: Vector Addition

  10. 1.7:Vector addition • Refer to Example 1.5.

  11. 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. 1.8: Components of vectors

  13. 1.8: Components of Vectors • Refer to Example 1.6.

  14. Finding a Vector’s Magnitude and Direction A = √(Ax2 + Ay2) tanθ = Ay/Ax

  15. 1.8: Calculations using components A = √(Ax2 + Ay2) tanθ = Ay/Ax

  16. 1.8: Calculations using components • Refer to Example 1.7

  17. 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 = Axi + Ayj + Azk • Refer to Example 1.9.

  18. 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: A•B = ABcosφ • If you know the components of the vectors: A•B = AxBx + AyBy + AzBz

  19. 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

More Related