Lect01 Ch 01-Scalars and Vectors

8/12/2019 Lect01 Ch 01-Scalars and Vectors

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CHAPTER 1:

SCALARS AND

VECTORS

MAS FIZA MUSTAFA

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03-3258 4972

013-7133158
mailto:[email protected]:[email protected]


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Scalars and Vectors

Problem Solving in Physics

Scalars Versus Vectors

The Components of a Vector

Adding and Subtracting Vectors

Unit Vectors *Scalar or dot product

*Vector or cross

Units of chapter:


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1-7 Scalars and Vectors

Scalar a numerical value. May be positive or negative.

Examples: speed, distance, height.

Vector a quantity with both magnitude and direction.

Examples: velocity, displacement (e.g., 10 feet north),force, magnetic field.


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For vectors in one

dimension, simple

additionand

subtractionare all thatis needed.

You do need to be

careful about the signs,as the figure indicates.


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When we indicate a vector, we draw an

arrow.

To indicate a vector with a written symbol,

we use boldface for the vector itself, with asmall arrow above it.

When we indicate a

magnitude, we use

Italic or modulus|r| = 0.5 mi


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3-2 Addition of VectorsGraphical Methods

The parallelogrammethod may also be used; here again the vectors must be tail-to-tip.


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3-3 Subtraction of Vectors, and Multiplication of a

Vector by a Scalar

In order to subtractvectors, we define the negative

of a vector, which has the same magnitude butpoints in the oppositedirection.

Then we add the negative vector.


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EXAMPLE 1- subtraction

+a b

= a-b

a-b

a b+ = a-b a-bor

b

b-a

-a

1

2


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3-3 Multiplication of a Vector by a Scalar

A vector can be multiplied by a scalar c; the result is a vector cthat has the

same direction but a magnitude cV. If cis negative, the resultant vector

points in the opposite direction.


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a

b

a

b


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x

y

x

y

x

y

x


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y

x

MAKE SURE THE ANGLE IS TAKEN

FROM POSITIVEX-AXIS !!!!


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A vector has a magnitude of 3.50 m and points in a direction that is counterclockwisefrom

the x-axis. Find the x and y components of this vector.

y

-x

EXAMPLE 2

x


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EXAMPLE 3A vector has a magnitude of 3.50 m and points in a direction that is 35Obelow x-axis. Find the x

and y components of this vector.

y

x

-y


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y

x

-y

-x

X = positive (+ve)

Y= positive (+ve)

III

X = negative (-ve)

Y= positive (+ve)

IV

X = positive (+ve)

Y= negative (-ve)

X = negative (-ve)

Y= negative (-ve)

III


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N

E

S

W

How to state the location of the angle?

North of east

N

E

S

W

East of North

Relative to the east

Relative to the North


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N

E

S

W

How to know the location of the angle?

West of North

N

E

S

W North of West

Relative to the north

Relative to the west


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N

E

S

W South of West

N

E

S

W West of South


Relative to the west

Relative to the south


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N

E

S

WEast of South

N

E

S

WSouth of East


Relative to the south

Relative to the east


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If the components (x and y) are given and u are asked to find the magnitude and direction

of the vector, it is just the same as the trigonometric concept.

Magnitude

Direction

direction


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EXAMPLE 4

Given the component of a vector is, Ax= -22.0m and Ay= 20.0m. Find the magnitude

and the direction of the vector. The direction of the vector must be relative to the

north.

Magnitude

Direction


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ContinueEXAMPLE 4

Note that = -42.4 is located in quadrant number 4

which is Relative to the East (South of East or BELOW x-AXIS)

butwe are asked to leave the direction relative to

the north, so

The final answer would be

N

E

S

W

West of North


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Vector A has a magnitude of 5 and a

direction angle of 40 above the x axis, andthat vector B has a magnitude of 4 and a

direction angle of 15 above the x axis. Find

vector C such that

(a) C = A + B

(b) C = A - B

Try This!!


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Lect01 Ch 01-Scalars and Vectors