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PHYS 201
Instructor : Dr. Hla
Class location: Walter 245
Class time: 12 – 1 pm (Mo, Tu, We, Fr)
Equation Sheet
You are allowed to bring an A4 size paper with your own notes
(equations, some graph etc.) to the midterm and final exam.
No equation will be given.
PHYS 201
Chapter 1
Power of Ten
Units
Unit Conversions
Basic Trigonometry
Graphical Analysis
Vectors
Vector Components
Prefixes
tera (T):
1012
1,000,000,000,000
giga (G) :
109
1,000,000,000
mega (M):
106
1,000,000
kilo (k):
103
1,000
centi (c):
10-2
1 / 100
milli (m):
10-3
1 / 1,000
micro (μ):
10-6
1 / 1,000,000
nano (n):
10-9
1 / 1,000,000,000
pico (p):
10-12
1 / 1,000,000,000,000
OU Atomic logo
30 nm
Basic Units
SI
CGS
BE
Length [L]
meter (m)
centimeter (cm)
Mass [M]
kilogram (kg)
gram (g)
slug (sl)
Time
second (s)
second (s)
second (s)
[T]
foot (ft)
Dimensions
All the other units are derived units.
Example:
Speed can be expressed with mph (miles per hour, or mi / h). It
is the unit of length divided by time (L / T).
Unit Conversion
Can't mix units when adding or subtracting - Need to convert
18 km + 5 mi is not 23
Can always multiply by 1
1 km =1000 m
1 = (1 km/1000m)
Can cancel units algebraically
Unit Conversion
Example 1
Convert 80 mi to km.
1 mi = 5280 ft
1 mi = 1.609 km
1 m = 3.281 ft
Example 2
Convert 60 mi/h to km/s, and m/s.
Example 3
Convert 60 mi/h to ft/s.
Unit Conversion
Example 4
You are driving on R33 near Logan with a speed of 26.67 m/s. The
speed limit there is 65 mph. Will you get a ticket because you are
speeding?
CLICKER!
Unit Conversion
Example 5
Convert 1000. ft/min into meters per second.
1). 0.197 m/s
2). 5.08 m/s
3). 24.5 m/s
4). 54.7 m/s
5). 169 m/s
6). 1540 m/s
7). 18300 m/s
Convert 1000. ft/min into meters per second.
1.
2.
3.
4.
5.
6.
7.
8.
0.0847 m/s
0.197 m/s
5.08 m/s
24.5 m/s
54.7 m/s
169 m/s
1540 m/s
18300 m/s
1 mi = 5280 ft
1 mi = 1.609 km
1 m = 3.281 ft
ft
1000
s
 1 min  1m 


  5.08m/s
 60s  3.281ft 
ANSWER!
CLICKER!
Unit Conversion
Example 6
A bucket has a volume of 1560 cm3. What is its volume in m3?
(1) 1.56x10-6 m3
(2) 1.56x10-4 m3
(3) 1.56x10-3 m3
(4) 1.56x10-2 m3
(5) 1.56x10-1 m3
(6) 1.56 m3
(7) 15.6 m3
(8) 1.56x103 m3
(9) 1.56x106 m3
(10) 1.56x109 m3
A bucket has a volume of 1560 cm3. What is its volume in m3?
(1) 1.56x10-6 m3 (2) 1.56x10-4 m3 (3) 1.56x10-3 m3
(4) 1.56x10-2 m3 (5) 1.56x10-1 m3 (6) 1.56 m3
(7) 15.6 m3
(8) 1.56x103 m3 (9) 1.56x106 m3
(0) 1.56x109 m3
ANSWER!
1560cm3 = 1560 cm*cm*cm (1m/100cm)*(1m/100cm)*(1m/100cm)
= 1.56x10-3 m3
How do you interpret cm-3 ?
1
cm 3
Negative exponent – inverse – place in denominator
Trigonometry
• Right Triangle
Sum of angles = 180
opposite angle = 90-θ
h  h h
2
a
2
o
Trigonometry
• Right Triangle
adjacent
cos  
hypotenuse
opposite
sin  
hypotenuse
opposite
tan  
adjacent
CLICKER!
Which is true?
2
2
2
2
2
2
1. A = B + C
C
2. B = A – C
3.
B
2
C2 = A2 + B

A
CLICKER!
Which is true?
1. A = C sin 
C
2. A = C cos 
B
3. B = C cos 

A
Example:
You walk a distance of 20m up to the top of a hill at an incline of 30°. What is the
height of the hill?
Note: DRAW PICTURE!
20m
h
h
sin  
20 m
h  ( 20 m) sin 30o
h  10 m
30º
What is the angle θ?
 4.5m 
tan 
  36.9
 6.0m 
1
DIMENSIONS
Length:
L
Mass:
M
Time:
T
Examples:
1). Speed: unit
(mi/h). Dimension: [L/T]
2). Area :
(ft2).
unit
3). Acceleration: Unit
4). Force:
Unit
Dimension: [L2]
(m/s2). Dimension: [L/T2]
(kg. m/s2) . Dimension: [ML/T2]
DIMENSIONS
Length:
L
Mass:
M
Time:
T
Dimensions of left and right side of an equation must be the same.
Example: x = ½ vt2
L = (L/T) (T2) = LT
[Dimensions at left and right are not the same.
WRONG equation.]
Example: x = ½ vt
L = (L/T) (T) = L
[Dimensions at left and right are the same.
CORRECT equation.]
Example:
CLICKER!
You are examining two circles. Circle 2 has a radius 1.7 times bigger than circle 1.
What is the ratio of the areas? Express this as the value of the fraction A2/A1.
A  r
(1) 1/1.7
(5) 1 / 1.7
(2) 1.7
(6) 1.7
(3) (1/1.7)2
(4) 1.72
A2 r22  (1.7r1 ) 2
2
 2 

(
1
.
7
)
A1 r1
r12
2
1
2
Slope of Function on
Graph
y
rise = Δy
• Slope = rise/run
• Up to right is positive
run = Δx
x
• Slope of curve at a point
– slope of tangent line
• Slope of straight line same
at any point
y
A
x
The slope at point B on this curve is _________ as you move to the right on
the graph.
CLICKER!
y
B
1. increasing
2. decreasing
3. staying the same
x
The slope at point B on this curve is _________ as you move to the right on
the graph.
CLICKER!
y
B
1. increasing
2. decreasing
3. staying the same
x
The slope at point B on this curve is _________ as you move to the right on
the graph.
y
1. increasing
2. decreasing
3. staying the same
B
x
Vectors
Vectors
Direction
length = magnitude
Some VECTOR quantities
-Displacement (m, ft, mi, km)
-Velocity (m/s, ft/s, mi/h, km/hr)
- Acceleration (m/s2, ft/s2)
-Force (Newton, N)
Vector Summation
A
B
+
A
C
=
C
B
+
=
Vector Summation
C = A +B
A
+
B
Two ways to sum the vectors:
Parallelogram method (1), and triangle method (2).
1)
2)
Vector Summation
C

A
B
C =
2
2
A + B
-1
 = tan
B
A
C = A +B
CLICKER!
Which is true?
1)
2)
A
3)
B
4)
C = A +B
CLICKER!
Which is true?
1)
2)
3)
4)
B
A
Vector Component
Y
A
AY

Ax
x
Example
30 N
o
60
40 N
An object is pulled by strings with 30 N and 40 N forces respectively as shown.
Find
(a) the magnitude of the net force.
(b) the direction of the net force (find the angle).
CAPA
-
Round up the numbers (e.g. 3.247321
3.25)
- Add the units: (e.g. cm, N (newton), deg (degree))
- Do not forget to put ‘-’ sign in vectors if the resultant vector is
in –x or –y direction.
- For m/s2
m/s^2