Chapter 3

1. Chapter 3 3-1 Introduction to scalar and vectors

2. Objectives • Distinguish between a scalar and a vector. • Add and subtract vectors by using the graphical method. • Multiply and divide vectors by scalars.

3. What is a scalar • A scalar is a physical quantity that has magnitude but no direction. Some examples are: speed, volume, the number of pages in your textbook

4. What is a vector? • A vector is a physical quantity that has both magnitude and direction. Some Examples are: displacement, velocity, acceleration

5. Let’s look at the video • Lets look at the video about scalars and vectors • In this book, scalar quantities are in italics. Vectors are represented by boldface symbols.

6. Resultant of vectors When adding vectors we need to make sure they have the same units and describe similar quantities. What is the resultant of a vector? A resultant vector represents the sum of two or more vectors.

7. Example#1 • Vectors can be added graphically A student walks from his house to his friend’s house (a), then from his friend’s house to the school (b). The student’s resultant displacement (c) can be found by using a ruler and a protractor.

8. Graphical addition • Lets watch the video about graphical addition

9. Properties of vectors • Vectors use a method called • Triangle Method of Addition • Vectors can be moved parallel to themselves in a diagram. • Thus, you can draw one vector with its tail starting at the tip of the other as long as the size and direction of each vector do not change. • The resultant vector can then be drawn from the tail of the first vector to the tip of the last vector

10. Properties of vectors • Vectors can be added in any order. • To subtract a vector, add its opposite. • Multiplying or dividing vectors by scalars results in vectors.

11. Lets watch a video about it • Lets watch a video about properties

12. Subtract, multiply ,and divide vectors • Lets watch how we can add and subtract vectors

13. Vector Addition • A variety of mathematical operations can be performed with and upon vectors. One such operation is the addition of vectors. Two vectors can be added together to determine the result (or resultant). This process of adding two or more vectors has already been discussed in an earlier unit. Recall in our discussion of Newton's laws of motion, that the net force experienced by an object was determined by computing the vector sum of all the individual forces acting upon that object. That is the net force was the result (or resultant) of adding up all the force vectors. During that unit, the rules for summing vectors (such as force vectors) were kept relatively simple. Observe the following summations of two force vectors:

14. These rules for summing vectors were applied to free-body diagrams in order to determine the net force (i.e., the vector sum of all the individual forces). Sample applications are shown in the diagram below. • In this unit, the task of summing vectors will be extended to more complicated cases in which the vectors are directed in directions other than purely vertical and horizontal directions. For example, a vector directed up and to the right will be added to a vector directed up and to the left. The vector sum will be determined for the more complicated cases shown in the diagrams below. • There are a variety of methods for determining the magnitude and direction of the result of adding two or more vectors. The two methods that will be discussed in this lesson and used throughout the entire unit are: • the Pythagorean theorem and trigonometric methods • the head-to-tail method using a scaled vector diagram

15. Homework • Do worksheet problems 2-6

16. Closure • Today we learn about scalars, vectors and how to add them , subtract them and more. • Next class we are going to continue with vector and its properties