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Micro-world Macro-world
Fall 2009
Instr: Stephen L. Olsen
What does “Physics” mean?
Greek:
φίσίσ
phisis
Chinese:
 Nature
物理
WU LI
“The logic of things”
or “How things work”
What kind of “things”?
Ordinary-sized objects::
apples:
footballs:
ukuleles:
etc.
Gigantic things
Earth
galaxies
etc.
Sun
Very tiny things
cells
molecules
atoms
quarks
Galileo Galilei
1562 - 1642
1st “modern” scientist
Example of how Galileo thought:
His experiments on motion on inclined planes
What if the 2nd track was
horizontal?
Aristotle ~300 BC
Physics book VII chapter 5
Forces are needed
to keep objects in
motion. A constant
force will have a
constant motion.
Galileo’s big idea
Forces are not needed
to keep objects in
motion. They are only
needed to change the
state of motion.
Actually, Galileo wasn’t first
Mozi ( 墨子 ) ~400BC
If there is no
opposing force,
motion will
never stop.
Object sliding on a surface
If there were no
friction the book
would keep sliding.
Angels are not needed to keep
planets moving in their orbits
Law of inertia
Discovered by Galileo, but as written by
Newton:
Every object perseveres in its state of rest,
or of uniform motion in a straight line, unless
it is so compelled to change that state of
motion by forces impressed thereon.
Comment on the Law of Inertia
•No mention of balls & tracks
•Applies to ordinary objects &
also huge objects like
galaxies and tiny objects
like atoms & quarks
Galileo knew nothing of galaxies or quarks,
but, thanks to his imagination, his insight,
based on observations of ordinary objects,
proved to be a universal truth.
Units
&
Reference Frames
Required for measurements/observations
English units
King’s foot
12 inches = 1ft
5280 ft = 1 mile
One meter of length
1 meter = 40 inches (1.1 yds)
10,000,000m
1m
About the distance from nose to the
outstretched finger (of a pretty big guy).
Centimeters & millimeters
1 centimeter = 1/100 meters
( radius of a penny)
1cm
1 millimeter = 1/1000 meters
( thickness of a dime)
1mm
 means
“approximately equal to”
1000 m = 1 kilometer (km)
1km  5/8 mile
Motion depends on the
circumstances of the observer (I)
backward
forward
•To us, both the red & blue cars move forward
•To someone in the red car, the blue car is
going backwards
Reference frames
aka Coordinate systems
z-axis
To describe the position
of an object: You need
to define a coordinate
system (reference frame)
& determine 3 coordinates
(vertical)
z
e.g.
x, y & z
reference point
(e.g. home plate)
z
x
x-axis
(e.g. the 1st baseline)
y
y-axis
(e.g. the 3rd baseline)
Choices of location of
the coordinate system
& directions of the axes
are up the observer.
Motion depends on the
circumstances of the observer (II)
z
y
x
•In the fish’s reference frame, it is the ground
that is moving
Some distances
Nose to finger
~1m
Back of the room
~10m
SNU library
~100m
SNU main gate
~1000m
Incheon
~50000m
Center of the Earth
~6400000m
Earth to Moon
~385000000m
Earth to Sun
~150000000000m
Next star
~40000000000000000m
We are only out to the next star & we
are already running out of space
Some small sizes
•
•
•
•
•
•
radius of a 10 won coin
~0.01 m
thickness of a 10 won coin
~0.001 m
thickness of a human hair
~0.000075 m
diameter of a red blood cell ~0.00000002 m
size of hydrogen atom
~0.00000000006 m
size of hydrogen nucleus ~0.0000000000000001 m
Again, the numbers become unwieldy
& use up a lot of space
Exponential logic
Exponential logic
powers of “2”
Area of a sheet of paper
21.5 cm
Area =28 cm x 21.5 cm
= 600 cm2
28 cm
Cut it in half
Area of the remaining sheet after 1
cut
21.5 cm
Area =28 cm x 21.5 cm
2
= 600 cm2
2
28 cm
2
= 600 (1/2)cm2
=300 cm 2
Cut it in half again
Area of the remaining sheet after 2
cuts
21.5 cm
2
Area =28 cm x 21.5 cm
2
2
= 600 cm2
2x2
28 cm
2
=600 cm 2 x(1/2)2
Cut it in
half again
=150cm2
Area of the remaining sheet after 3
cuts
21.5 cm
2
Area =28 cm x 21.5 cm
2x2
2
= 600 cm2
2x2x2
=600 cm 2 x(1/2)3
1 28 cm
2 2
=75cm2
Cut it in
half again
After 12 times
28 cm
26
21.5 cm
26
Area =28 cm x 21.5 cm
26
26
= 600 cm2
26x26
=600 cm 2 x(1/2)12
= 600 cm2
4096
=0.15 cm2
Smallest piece of
paper I can handle
Imagine we did it 70 times
28 cm
235
21.5 cm
235
Area =28 cm x 21.5 cm
235
235
= 600 cm2
235x235
=600 cm 2 x(1/2)70
=600 cm2 x
1
1,180,591,620,717,411,3??,???
= 5.1 x10-19 cm2
(about ½ the area of an atom)
1
1,180,591,620,717,411,3??,???
is unwieldy
(다루기 힘든, 꼴 사나운)
Difficult to manage
(1/2)70
Is more tractable
Tractable
easy to manage
Powers of 10
$ 100.0 = $ 10.00 x 10
Move the decimal
point 1 place to the left
“penny”
&
multiply
by 10
“dime”
$0.01 = $00.1 x 1/10
Move the decimal
point 1 place to the right
&
divide
by 10
Positive powers of 10
19
2
4
5
6
7
8
10
11
15000000000.0 xx10
150000000000.
150000000000
15000000.0000
1500000.00000
150000.000000
15000.0000000
1500.00000000
150.0000000000
15.0000000000
1.50000000000
1500000000.00
10x10
10
11 jumps to the left
 +11 in the exponent
= 1.5 x 1011
Some distances
•
•
•
•
•
•
•
•
•
Nose to finger
~1 m
The back of the room
~10 m
SNU Library
~100 m
SNU Main gate
~1000 m
~5.0
x 104mm
Incheon
~50000
Center of Earth
~6400000
~6.4 x 106 m
m
~3.86 x 108 mm
Earth to Moon
~386,000,000
Earth to Sun
~150000000000
~1.5 x 1011 m m
Next star
~40000000000000000
~4.0 x 1016 m m
nomenclature
• 103 = 1 thousand (kilo)
• 106 = 1 million (mega)
• 109 = 1 billion (giga)
• 1012 = 1 trillion (tera)
Small numbers
1 penny = $0.01
1 dime= $0.10
1 penny = 1/10th of a dime
$0.01 = $0.10x(1 /10)
Moving the decimal point 1 place to the
right is the same as multiplying by 10
Negative powers of 10
-11
-1x10-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
0.00000000006 x10
00.0000000006
000.000000006
0000.00000006
00000.0000006
000000.000006
0000000.00006
00000000.0006
000000000.006
0000000000.06
00000000000.6
000000000006.x
10
1/10
11 jumps to the right  -11 in the exponent
= 6.0 x 10-11
Some small sizes
•
•
•
•
•
•
radius of a 10 won coin
~0.01 m
thickness of a 10 won coin
~0.001 m
thickness of a human hair
~0.000075
~7.5
x 10-5 m
x 10-8 m m
diameter of a red blood cell ~2.0
~0.00000002
size of hydrogen atom
~0.00000000006
~6.0 x 10-11 m m
~1.0 x 10-15 m
size of hydrogen nucleus ~0.000000000000001
m
More nomenclature
• 10-2 = centi• 10-3 = milli• 10-6 = micro- (m)
• 10-9 = nano• 10-12 = pico-
exponents are very important
Distance to the Sun: 1.5 x 1011m
Light from the sun
takes 8 minutes to
get here
8 minutes
from now
Exponents differ by 5
Distance to next star: 4 x 1016 m
Light from the next
star takes 4 years to
get here
4 years from now?
Multiplying large numbers
Use the rule:
10a+b
(A x 10a ) x (B x 10b) =(AxB) x (10a x 10b)
Number of people
x
average income/person
301,000,000
x
$ 40,100
on
1/8/07
3.01x108
x
$ 4.01x104
In the US
=
= (3.01 x $4.01) x (108 x 104)
= $12.1 x
108+4
=$12.1 x
1012
= $1.21 x 1013
Sum of everyone’s income
dividing large numbers
10a-b
A x 10a x 10-b
Ax10a = A x 10a
=
b
b
Bx10
B 10
B
move b upstairs & change sign
US national debt =
# of persons in US
$8.60 x 1012
= 3.01 x 108 persons
=
= $2.86 x 1012- 8 /person
$8,598,000,000,000
301,000,000 persons
$8.60 x 1012
3.01
108 persons
= $2.86 x 104/person
(= $28,600/person)
on
818/07
$28,600 (ladies not included)