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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).

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Chapter 1

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  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

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