1. week 2
Vectors in Physics

2. Vector vs. Scalar Review
All physical quantities encountered in this text will be either a scalar or a vector
A vector quantity has both magnitude (size) and direction
A scalar is completely specified by only a magnitude (size)

3. Vector Notation When handwritten, use an arrow:
When printed, will be in bold print with an arrow:
When dealing with just the magnitude of a vector in print, an italic letter will be used: A
Italics will also be used to represent scalars

4. Properties of Vectors Equality of Two Vectors
Two vectors are equal if they have the same magnitude and the same direction
Movement of vectors in a diagram
Any vector can be moved parallel to itself without being affected

5. More Properties of Vectors
Negative Vectors
Two vectors are negative if they have the same magnitude but are 180° apart (opposite directions)
Resultant Vector
The resultant vector is the sum of a given set of vectors

6. Adding Vectors Geometrically (Triangle or Polygon Method)
Choose a scale
Draw the first vector with the appropriate length and in the direction specified, with respect to a coordinate system
Draw the next vector using the same scale with the appropriate length and in the direction specified, with respect to a coordinate system whose origin is the end of vector and parallel to the coordinate system used for

7. Graphically Adding Vectors, cont.
Continue drawing the vectors “tip-to-tail”
The resultant is drawn from the origin of to the end of the last vector
Measure the length of and its angle
Use the scale factor to convert length to actual magnitude

8. Graphically Adding Vectors, cont.
When you have many vectors, just keep repeating the process until all are included
The resultant is still drawn from the origin of the first vector to the end of the last vector

9. Notes about Vector Addition
Vectors obey the Commutative Law of Addition
The order in which the vectors are added doesn’t affect the result

10. Vector Subtraction Special case of vector addition
Add the negative of the subtracted vector
Continue with standard vector addition procedure

11. 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

12. 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:

13. 3-2 The Components of a Vector
Can resolve vector into perpendicular components using a two-dimensional coordinate system:
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14. 3-2 The Components of a Vector
Length, angle, and components can be calculated from each other using trigonometry:

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

20. 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.

24. Figure 3.9 (below)

26. 3-3 Adding and Subtracting Vectors
Adding Vectors Using Components:
Find the components of each vector to be added.
Add the x- and y-components separately.
Find the resultant vector.

27. 3-3 Adding and Subtracting Vectors

28. 3-3 Adding and Subtracting Vectors
Subtracting Vectors: The negative of a vector is a vector of the same magnitude pointing in the opposite direction. Here,

30. 3-4 Unit Vectors
Unit vectors are dimensionless vectors of unit length.

32. 3-4 Unit Vectors
Multiplying unit vectors by scalars: the multiplier changes the length, and the sign indicates the direction.

43. Right hand rule cross product

45. Summary of Chapter 3 Scalar: number, with appropriate units
Vector: quantity with magnitude and direction
Vector components: Ax = A cos θ, By = B sin θ
Magnitude: A = (Ax2 + Ay2)1/2
Direction: θ = tan-1 (Ay / Ax)
Graphical vector addition: Place tail of second at head of first; sum points from tail of first to head of last