1. © 2013 Pearson Education, Inc. Chapter Goal: To learn how vectors are represented and used. Chapter 12 Vectors Slide 3-2

2. © 2013 Pearson Education, Inc.  A quantity that is fully described by a single number is called a scalar quantity (i.e., mass, temperature, volume).  Time - Scalar quantities often refer to time; the measurement of years, months, weeks, days, hours, minutes, seconds, and even milliseconds.  Volume - Scalar quantity can refer to the volume, as in how much of something is present. Tons to ounces to grams, milliliters and micrograms are all scalar quantities, as long as they are applied to the medium being measured and not the movement of the medium. Vectors Slide 3-16

3. © 2013 Pearson Education, Inc. SPEED OF A PLANE SCALAR

4. © 2013 Pearson Education, Inc. Scalar A SCALAR is ANY quantity that has MAGNITUDE, but NOT a direction associated with it. Magnitude – A numerical value with units. Scalar Example Magnitude Speed20 m/s Distance10 m Age15 years Heat1000 calories

5. © 2013 Pearson Education, Inc. Scalar A SCALAR is ANY quantity that has MAGNITUDE, but NOT a direction associated with it. Magnitude – A numerical value with units. Any measurement that consists of a single number is a scalar. 72 °F 500 milliliters 1.5 volts 6 hours, 30 minutes (consider this as 6.5 h)

6. © 2013 Pearson Education, Inc. Vector A VECTOR is ANY quantity that has BOTH MAGNITUDE and DIRECTION. VectorMagnitude & Direction Velocity20 m/s, N Acceleration10 m/s/s, E Force5 N, West Vectors are typically illustrated by drawing an ARROW above the symbol. The arrow is used to convey direction and magnitude.

7. © 2013 Pearson Education, Inc. A quantity having both a magnitude and a direction is called a vector quantity. The geometric representation of a vector is an arrow with the tail of the arrow placed at the point where the measurement is made. We label vectors by drawing a small arrow over the letter that represents the vector, i.e.,: for position, for velocity, for acceleration.

8. © 2013 Pearson Education, Inc. Chapter 12 Preview Slide 3-3

9. © 2013 Pearson Education, Inc. The length of the arrow represents the size or magnitude of the quantity. The arrowhead shows its direction 50N = (50 Newtons) 50N N 55°

10. © 2013 Pearson Education, Inc. PAGE 277. 12A.1 #1A 135° 30 N

11. © 2013 Pearson Education, Inc. PAGE 277. 12A.1 #1B 25ms -1

12. © 2013 Pearson Education, Inc. HOMEWORK page 277 (12A.1) Numbers 1 – 3 On number 3, use the scale: 1cm = 10 newtons 1cm = ms -1 1cm = 1 unit 1cm = 30 kmh -1

13. © 2013 Pearson Education, Inc. CHAPTER 12. A.2

14. © 2013 Pearson Education, Inc. Vector Notation  A vector variable is represented by a small arrow over the top of the variable.  Some texts use boldface for vectors, but that can be hard to distinguish on some backgrounds. Our text uses both boldface and an arrow.  The magnitude (OR LENGTH) of a vector is a scalar.  It is represented as the absolute value of the vector, or just the variable without the vector symbol.

15. © 2013 Pearson Education, Inc. Vector Notation  The magnitude or length could be represented by:  This vector originates at O. (Initial Point)  This vector terminates at A (Terminal Point) O A a Originates at the origin (0,0) POSITION VECTOR

16. © 2013 Pearson Education, Inc. Q Terminal Point direction is this angle It is easiest to find a vector with initial point at the origin and terminal point (x, y). P Initial Point A vector whose initial point is the origin is called a position vector is a Position vector

17. © 2013 Pearson Education, Inc. A vector is a quantity that has both magnitude and direction. It is represented by an arrow. The length of the vector represents the magnitude and the arrow indicates the direction of the vector. Two vectors are equal if they have the same direction and magnitude (length). Blue and orange vectors have same magnitude but different direction. Blue and green vectors have same direction but different magnitude. Blue and purple vectors have same magnitude and direction so they are equal.

18. © 2013 Pearson Education, Inc. Parallel and Geometric Negative Vectors  Equal Vectors are parallel IF they point in the same direction AND equal in length. You can be NOT equal and parallel  Vectors that point in opposite directions are negatives. A B

19. © 2013 Pearson Education, Inc. HOMEWORK page 278 (12A.2) Numbers 1 – 3