03_lectureoutline week 2 [compatibility mode]

8/6/2019 03_LectureOutline Week 2 [Compatibility Mode]

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ec ors n ys cs

Copyright 2010 Pearson Education, Inc.


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. All physical quantities encountered in this

text will be either a scalar or a vector

A vector quantity has both magnitude

A scalar is completely specified by only a

magnitude (size)



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en an wr tten, use an arrow:

When rinted will be in bold rint with anr

arrow:

Ar

vector in print, an italic letter will be used:

Italics will also be used to represent scalars



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Equality of Two Vectors

Two vectors are e ual if the have the samemagnitude and the same direction

Any vector can be moved parallel to itselfw ou e ng a ec e



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egat ve ectors

Two vectors are negative if they have thesame magnitude but are 180apart (oppositedirections) r r r r

Resultant Vector

;= + =

The resultant vector is the sum of a given set

of vectors

= +R A Br r r



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Adding Vectors Geometrically

(Triangle or Polygon Method) oose a sca e

Draw the first vector with the appropriate lengthan n t e rect on spec e , w t respect to acoordinate system

raw e nex vec or us ng e same sca e wthe appropriate length and in the direction,

whose origin is the end of vector and parallelAr

r



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Graphically Adding Vectors,

cont. on nue raw ng e vec ors p- o- a

The resultant is drawn from the origin of to the end of

Measure the length of and its angle Use the scale factor to convert length to actual magnitude

Ar

Rr



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3-1 Scalars Versus Vectors

Scalar: number with units

Vector: quantity with magnitude and direction

How to et to the librar : need to know how far andwhich way



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3-2 The Com onents of a Vector

Even though you know how far and in which

y , y u y

to walk there in a straight line:



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3-2 The Com onents of a VectorCan resolve vector into perpendicular components using a two-dimensional coordinate system:


Page 59Page 60


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3-2 The Components of a Vector

Length, angle,and componentscan becalculated fromeach other usin

trigonometry:



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3-2 The Components of a Vector

Signs of vector components:



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.


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3-3 Addin and Subtractin Vectors

Adding Vectors Using Components:1. Find the components of each vector to be

added.

2. Add the x- and y-components separately.

3. Find the resultant vector.



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Subtracting Vectors: The negative of a vector is

a vector of the same magnitude pointing in the

opposite direction. Here, .D= A B

r r



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3-4 Unit Vectorsii

Unit vectors are dimensionless vectors of unit

.



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$i, j, k$ $


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3-4 Unit Vectors

Multiplying unit vectors by scalars: the multiplier

changes the length, and the sign indicates the

direction.



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Right hand r le cross


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Right hand rule cross

pro uct


S f Ch t 3


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Summar of Cha ter 3

Vector: quantity with magnitude and direction Vector components: Ax= A cos , By= B sin

agn tu e: A = Ax

+ Ay

= -1

Graphical vector addition: Place tail of secondat ea o rst; sum po nts rom ta o rst tohead of last


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