6B - Vectors

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Physical Quantities, Units and MeasurementPhysical Quantities, Units and Measurement

T H E M E O N E : M E A S U R E M E N T

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Scalar & Vector Quantities

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1.4 Scalars and Vectors

• Scalar quantities are quantities that havemagnitude only. Two examples are shown elow!

Measuring Mass Measuring Temperature

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• Scalar quantities are added or sutracted y usingsimple arithmetic.

"xample! # $g plus % $g gives the answer 1& $g

' (

# $g

% $g

1& $g

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• Vector quantities are quantities that have othmagnitude and direction

Magnitude ( 1&& )

*irection ( +et

- orce Arrgh

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• "xamples o scalars and vectors

/calars 0ectors

distance displacement

speed velocity

mass weight

time acceleration

pressure orce

energy momentum

volume

density

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Vectors

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Vector Addition

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Adding Vectors using Gra!ical Met!od• Parallel vectors can e added arithmetically

)

# )

% ) # )

)

)

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Adding Vectors using Gra!ical Met!od• )on2parallel vectors are added y graphical

means using the parallelogram law3 0ectors can e represented graphically y arrows

3 The length o the arrow represents the magnitude o the

vector

3 The direction o the arrow represents the direction o the

vector

3 The magnitude and direction o the resultant vector can e

ound using an accurate scale drawing

4.& cm &.& )*irection ( right

≡

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• The arallelogra" la# o$ %ector addition statesthat i two vectors acting at a point are

represented y the sides o a parallelogram

drawn rom that point, their resultant isrepresented y the diagonal which passes through

that point o the parallelogram


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Head&to&tail Met!od 'Alternati%e "et!od(• To add vectors A and B

3 place the starting point o B at the ending point o A

3 The vector sum or resultant R is the vector 5oining the

starting point o vector A to the ending point o B3 Conversely, R can also e otained y placing the

starting point o - at the ending point o 6

3 )ow the resultant is represented y the vector 5oining

the starting point o 6 to the ending point o -

• /ee next slide

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-

6

-

6

-6

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C h a p t e r 1Vectors: Graphical method

• A light aircraft is flying with a velocity relative to

the air of 200kmh! in a direction due north"

#here is a wind $lowing from a direction of %00

north of west at 0kmh!

"• 'alculate the velocity of the aircraft relative to

the ground"

• Ans: vmag ( !)*kmh!+ vdirection ( 22

0 east of north

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Vector Su$traction

A ,- (

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'omponents of Vectors• A num$er of vectors which are added together to

give a single resultant are called the

components of the resultant"

•."g /etermine the components of the velocityvector !0 ms 1 %0°"

• 3 ( ")4+ y ( 54

1

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esolution of Vectors

• #he sum of two or more vectors is a single

vector called the resultant" #hey are drawn from

the tail of the first vector to the head of the last

vector"

1

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."g!• esolve the vector $elow into its

components"

1

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."g 2• esolve the vector $elow into its

components

• x coordinate = 2 ×sin(60°) =

y coordinate = 2 ×cos(60°) = 2(½)=1

1

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."g %• A cruise sails at %0kmh! in a north

easterly direction 6Ѳ = 450)" 7hat is its

speed in an easterly direction8 6Give ans

in ms to 2s"f"9"

• Ans: 2!kmh! ( 5" ms

1

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1. /calar quantities are quantities that only havemagnitudes

. 0ector quantities are quantities that have oth

magnitude and direction

7. Parallel vectors can e added arithmetically#. )on2parallel vectors are added y graphical

means using the parallelogram law

5" #he direction or angle of a vector is always

measured from the horiontal"*" #rigonometric functions and the ;ythagorean

#heorem are used to calculate the magnitude and

direction of resultant vectors"

1

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• ?@

'A?@ #>A to get the direction"

•

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6B - Vectors

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