TOPIC 2

1. TOPIC 2 Physical Quantities: Scalar and Vector Quantities

2. Lecture Outline • Scalar Quantities • Vector Quantities • Addition of Vector Quantities • Application of Vector Quantities

3. Lecture Objectives • After this lecture, students will be able: • To define scalar quantities • To define vector quantities • To analyze vector addition using graphical approach • To analyze vector addition using vector components

4. Scalars Scalar quantities are those which are described solely by their magnitudeSome examples are: Mass e.g. 14 [kg], 36 [lbs], … Time e.g. 10 seconds, 40 minutes, … Volume e.g. 1000 cm3, 4 litres, 12 gallons Temperature e.g 14 oF , 25 oC, … Voltage e.g. 9 Volts, etc

5. Vectors Vector quantities are those which need to be described by BOTH magnitude and direction Some of the most common examples which we will encounter are: Velocity e.g. 100 [mi/hr] NORTH Acceleration e.g. 10 [m/sec2] at 35o with respect to EAST Force e.g. 980 [Newtons] straight down (270o) Momentum e.g. 200 [kg m/sec] at 90o.

6. Vectors recall • Quantities with magnitude and direction • Magnitude • Size or quantity in unit of measurement • 10 meters, 5 Newtons • Direction • Compass direction: North, Southeast • Angle: 25o from the positive x axis • Examples • Distance—5 miles North • Acceleration—10m/s2 down • Force—100 Newton at an angle of 30o above the horizontal

7. Vector • an arrow drawn to scale used to represent a vector quantity • vector notation

8. Ways to add vectors • Graphically • Tip to tail method • Parallelogram • Using components

9. Graphical addition of vectors Arrange tail of vector B on tip of vector A. The vector sum C, called the resultant, is drawn from the tail of vector A to the tip of vector B. The order of addition does not matter. B A C C = A + B

10. Tip-to-Tail Method • Example 1: Add these vectors using the tip-to-tail method. +

11. Tip to Tail Method

12. Parallelogram Method A C B B (parallel) Note: B has direction and size, but starting point is arbitrary

13. Subtraction and Multiplication of Vector 1. The negative of a vector is a vector of the same magnitude but in the opposite direction. Thus vector v = 5 m/s due east, then –v = 5 m/s due west. 2. In order to subtract one vector from another, rewrite the problem s that the rules of vector addition can be applied. Example : A – B can be written as A + (-B)

14. Vector components y A vector R which lies at some angle q to an axis has two perpendicular components, Rxand Ry which lie on the axes. If you draw a straight line from the tip of vector R to the axis, this distance along the axis is the magnitude of the component. R Ry q x Rx

15. Resolving a vector into components y Applying trigonometry, the components of the vector R can be defined. Rx = Rcos(q) Ry = Rsin(q) tan q = Ry / Rx R = √(Rx2 + Ry2) R Ry q x Rx

17. Analytical addition of vectors • To add vectors analytically, add their components • Resolve individual vectors to be added into x and y or North and East components using trig • Add all of the x components • Add all of the y components • Find the magnitude of the Resultant (the vector sum) by taking the square root of the sum of the squares of the x and y components • Find the angle of the Resultant using trig

18. Vector Summation B A C B

19. Summary • In nature, there are two types of quantities, scalars and vectors • Scalars have only magnitude, whereas vectors have both magnitude and direction. • The vectors we learned about are distance, velocity, acceleration, force, and momentum • The scalars we learned about are time, and Energy.