PPMF 101 Lecture 3 Scalars Vectors 1 Scalars

PPMF 101– Lecture 3 Scalars & Vectors 1

Scalars & vectors Ø Scalars – quantities with only magnitudes l l Eg. Mass, time, temperature Mathematics - ordinary algebra Ø Vectors – quantities with magnitudes & directions l l Eg. Displacement, velocity, acceleration Mathematics - vector algebra 2

Vector notations – symbols of vector quantities Ø A short arrow is drawn over the symbol of a vector quantity. Ø E. g. displacement Velocity r v 3

Vector representations Ø A vector quantity is represented by an arrow to represent its magnitude (the length of the arrow) and direction (direction of the arrowhead) Ø Eg. 1. A man walks 5 m to the west. His displacement can be represented by the following arrow. 4

Ø Eg. 2. A car moving 50 km/h to the east. The velocity vector of the car can be represented by the following arrow: 5

Addition of Vectors – Graphical Methods – 1 Dimension 6

Addition of Vectors- Graphical Method – 2 Dimensions 7

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Subtraction of Vectors 9

Adding Vectors by Components – Resolving Vectors 10

Two ways to specify a vector 1. Give its componens, Vx and Vy Ø 2. Give its magnitud V and angle it makes with positive x – axis Ø We can shift from one description to the other by using theorem of Pythagoras and definition of tangent Ø 11

Resolving a vector = finding components of a vector 12

Example 1 Ø A man walks 20 m to the east and then he stops and walks 5 m to the west. What is the man’s Ø a) total distance travelled? Ø b) total displacement? 13

Example 2 Ø An aeroplane flies 200 km to the north and then 300 km to the east. Ø a) What is the total distance travelled by the plane? Ø b) What is the total displacement of the plane? 14