1. © 2007 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials. Lecture Outlines Chapter 3 Physics, 3 rd Edition James S. Walker

2. Chapter 3 Vectors in Physics

3. Units of Chapter 3 Scalars Versus Vectors The Components of a Vector Adding and Subtracting Vectors Unit Vectors Position, Displacement, Velocity, and Acceleration Vectors Relative Motion

4. 3-1 Scalars Versus Vectors Scalar: number with units Vector: quantity with magnitude and direction How to get to the library: need to know how far and which way

5. 3-2 The Components of a Vector Even though you know how far and in which direction the library is, you may not be able to walk there in a straight line:

6. 3-2 The Components of a Vector Can resolve vector, defined by its length r and its direction angle θ, into perpendicular components (r x, r y ) using a two-dimensional coordinate system:

7. 3-2 The Components of a Vector Length, angle, and components can be calculated from each other using trigonometry:

8. Figure 3-4 A vector and its scalar components

9. Example 3-1a Determining the Height of a Cliff

10. Example 3-1b Determining the Height of a Cliff

11. Figure 3-5 A vector whose x and y components are positive

12. 3-2 The Components of a Vector Signs of vector components:

13. Figure 3-7 Vector direction angles

14. Figure 3-8 The sum of two vectors

15. 3-3 Adding and Subtracting Vectors Adding vectors graphically: Place the tail of the second at the head of the first. The sum points from the tail of the first to the head of the last.

16. Figure 3-10 Identical vectors A at different locations

17. Figure 3-11 A + B = B + A

18. Figure 3-12 Graphical addition of vectors

19. 3-3 Adding and Subtracting Vectors Adding Vectors Using Components: 1. Find the components of each vector to be added. 2. Add the x- and y-components separately. 3. Find the resultant vector.

20. 3-3 Adding and Subtracting Vectors

21. Subtracting Vectors: The negative of a vector is a vector of the same magnitude pointing in the opposite direction. Here, D = A – B.

22. 3-4 Unit Vectors Unit vectors are dimensionless vectors of unit length.

23. 3-4 Unit Vectors Multiplying unit vectors by scalars: the multiplier changes the length, and the sign indicates the direction.

24. 3-5 Position, Displacement, Velocity, and Acceleration Vectors Position vector r points from the origin to the location in question. The displacement vector Δr points from the original position to the final position.

25. Figure 3-18 Position vector

26. 3-5 Position, Displacement, Velocity, and Acceleration Vectors Average velocity vector: (3-3) So v av is in the same direction as Δr.

27. 3-5 Position, Displacement, Velocity, and Acceleration Vectors Instantaneous velocity vector is tangent to the path:

28. 3-5 Position, Displacement, Velocity, and Acceleration Vectors Average acceleration vector is in the direction of the change in velocity:

29. Figure 3-23 Average acceleration for a car traveling in a circle with constant speed

30. 3-5 Position, Displacement, Velocity, and Acceleration Vectors Velocity vector is always in the direction of motion; acceleration vector can point anywhere:

31. 3-6 Relative Motion The speed of the passenger with respect to the ground depends on the relative directions of the passenger’s and train’s speeds:

32. Figure 3-26 Adding velocity vectors

33. 3-6 Relative Motion This also works in two dimensions:

34. Figure 3-28 Vector addition used to determine relative velocity

35. Figure 3-29 Reversing the subscripts of a velocity reverses the corresponding velocity vector

36. Summary of Chapter 3 Scalar: number, with appropriate units Vector: quantity with magnitude and direction Vector components: A x = A cos θ, A y = A sin θ Magnitude: A = (A x 2 + A y 2 ) 1/2 Direction: θ = tan -1 (A y / A x ) Graphical vector addition: Place tail of second at head of first; sum points from tail of first to head of last

37. Component method: add components of individual vectors, then find magnitude and direction Unit vectors are dimensionless and of unit length Position vector points from origin to location Displacement vector points from original position to final position Velocity vector points in direction of motion Acceleration vector points in direction of change of motion Relative motion: v 13 = v 12 + v 23 Summary of Chapter 3