PPMF101– Lecture 3PPMF101– Lecture 3

Scalars & VectorsScalars & Vectors

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Scalars & vectorsScalars & vectors

Scalars – quantities with only magnitudesScalars – quantities with only magnitudes Eg. Mass, time, temperatureEg. Mass, time, temperature Mathematics - ordinary algebraMathematics - ordinary algebra

Vectors – quantities with magnitudes & Vectors – quantities with magnitudes & directionsdirections Eg. Displacement, velocity, accelerationEg. Displacement, velocity, acceleration Mathematics - vector algebraMathematics - vector algebra

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Vector notations – symbols of Vector notations – symbols of vector quantitiesvector quantities

A short arrow is drawn over the symbol of A short arrow is drawn over the symbol of a vector quantity. a vector quantity.

E.g. displacement E.g. displacement rr VelocityVelocity v v

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Vector representationsVector representations

A vector quantity is represented by an A vector quantity is represented by an arrow to represent its magnitude (the arrow to represent its magnitude (the length of the arrow) and direction length of the arrow) and direction (direction of the arrowhead)(direction of the arrowhead)

Eg.1. A man walks 5 m to the west. His Eg.1. A man walks 5 m to the west. His displacement can be represented by the displacement can be represented by the following arrow.following arrow.

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

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Addition of Vectors – Graphical Addition of Vectors – Graphical Methods – 1 DimensionMethods – 1 Dimension

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Addition of Vectors- Graphical Method – 2 Addition of Vectors- Graphical Method – 2 DimensionsDimensions

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Subtraction of VectorsSubtraction of Vectors

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Adding Vectors by Components – Adding Vectors by Components – Resolving VectorsResolving Vectors

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Two ways to specify a vectorTwo ways to specify a vector 1. Give its componens, V1. Give its componens, Vxx

and Vand Vyy

2. Give its magnitud V and 2. Give its magnitud V and angle angle it makes with it makes with positive x – axispositive x – axis

We can shift from one We can shift from one description to the other by description to the other by using theorem of Pythagoras using theorem of Pythagoras and definition of tangentand definition of tangent

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Resolving a vector = finding Resolving a vector = finding components of a vectorcomponents of a vector

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Example 1Example 1 A man walks 20 m to the east and then he stops A man walks 20 m to the east and then he stops

and walks 5 m to the west. What is the man’s and walks 5 m to the west. What is the man’s a) total distance travelled?a) total distance travelled? b) total displacement?b) total displacement?

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Example 2Example 2

An aeroplane flies 200 km to the north and An aeroplane flies 200 km to the north and then 300 km to the east. then 300 km to the east.

a) What is the total distance travelled by a) What is the total distance travelled by the plane? the plane?

b) What is the total displacement of the b) What is the total displacement of the plane?plane?

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