CH0102part2 - Key to the success in this class Time You...

Key to the success in this class
Time : You need to spend enough hours on it.
Learn smartly : Study groups, office hour, etc.
Practice, practice, and practice: HMWK, End-of-
chapter problems
Pre-lecture: Read the book before
Post-lecture: Read the book (slides) after
Train yourself to think scientifically and
independently

Chapter 1: Vectors VS Scalars
•
Concept of vector (VS scalar)
•
Vector addition
•
Unit vector notation
•
Components of vectors
–
Vector addition using components
–
Vector decomposition
•
* Products of vectors (covered in later chapters)

Vectors: Magnitude and Direction
•
Vectors show magnitude and displacement, drawn as a ray.
A physics vector is quantity that
has both magnitude
(how long/how fast, etc)
and direction
Confused? You won’t be the only
One. Be patient and we will come
back to this often
If lost in a desert (forest) at P1, which quantity
should you try to maximize
(distance or displacement)

Vector addition (consider your daily commuting route)
•
Vectors may be added graphically, “head to tail.”

Vector addition Example:
•
A traveler hiked 1.00km north, then 2.00km to the west.
•
What is the displacement (d) his ending position from the starting
position?

Vector addition Example:
•
A traveler hiked 1.00km north, then 2.00km to the west.
•
What is the displacement (d) his ending position from the starting
position?
d
2
= (1.00 km )
2
+(2.00 km )
2
d
2
= 5.00 km
2
d = 5.00 km
tgf =
2.00 km
1.00 km
= 2.00
f = tg
- 1
(2.00) = 63.4
o

Components of vectors
•
Manipulating vectors graphically is insightful but difficult when
striving for numeric accuracy. Vector components provide a numeric
method of representation.
•
Any vector is built from an x component and a y component (and z).
•
Any vector may be “decomposed” into its x component using V *cos θ
and its y component using V *sin θ (where θ is the angle the vector V
sweeps out from 0°).

Unit vectors—Figures
•
Assume vectors of
magnitude 1 with no units
exist in each of the three
standard dimensions.
•
The x direction is termed i ,
the y direction is termed j ,
•
A vector is subsequently
described by a scalar times
each component.
A = A
x
i + A
y
j
= A
cos θ
i + A
sin θ
j
•
Refer to Example 1.9.
cos θ

Vector addition Example II:
A traveler hiked 5km at 37 degrees relative to the x-axis,
then 10km at 53 degrees relative to the x-axis. What is the resultant
Displacement?
37
o
53
o
ρ
d
1
ρ
d
2
ρ
d = ?
θ
x
y
DECOMPOSE first!

Vector addition Example II:
ρ
d
1
= (5 km )cos37
o
ö
x +(5 km )sin37
o
ö
y
= (4 km )
ö
x +(3 km )
ö
y
r
d
2
= (6 km )
ö
x +(8 km )
ö
y
r
d =
r
d
1
+
r
d
2
= (10 km )
ö
x +(11 km )
ö
y
tgq =
11 km
10 km
=1.1
q = tg
- 1
(1.1) = 47.7
o
A traveler hiked 5km at 37 degrees relative to the x-axis,
then 10km at 53 degrees relative to the x-axis. What is the resultant
Displacement?
37
o
53
o
ρ
d
1
ρ
d
2
ρ
d = ?
θ
x
y

Q1.1
A. E
x
= E cos β , E
y
= E sin β
B. E
x
= E sin β , E
y
= E cos β
C. E
x
= – E cos β , E
y
= – E sin β
D. E
x
= – E sin β , E
y
= – E cos β
E. E
x
= – E cos β , E
y
= E sin β
What are the x –
and y –components
of the vector
r
E ?

A1.1
A. E
x
= E cos β , E
y
= E sin β
B. E
x
= E sin β , E
y
= E cos β
C. E
x
= – E cos β , E
y
= –