It may seem like physics is here to make your lives harder. However, one of our prime motivations in this class will be to see how physics actually makes things easier.
You'll hear a lot of different answers to the question: what is physics? You can decide for yourselves as we go through this course.
The goals of physics
Predict
everything (i.e. the future of the universe)
If you can't, then isolate parts of the system until you can
The divisions of Physics ca. 2020
Classical
Modern
Mechanics
Quantum Physics
Electricity
Cosmology
Magnetism
Nuclear
Thermodynamics
Fluids
Condensed Matter
Waves
Bio-Physics
Optics
How do we do this?
The Scientific Method:
Question → hypothesis → testing → analysis
Physics: Division of Labor
Some physicists work on
theory. Others do
experiments. While they have different approaches to things, they basically agree on a few major points.
Theories must be verifiable by experiment
Phenomena can be described mathematically
Experiments must involve measurements
Measurement: Units
Here's Rob. He makes beer. These are some of the common (and uncommon) units used to describe volume. Every time you drink one his beers, you hope that he got his units correct!
liter
hectoliter
drop
cup
pint
barrel
gallon
quart
fluid ounce
tablespoon
teaspoon
inch$^3$
acre-foot
stere
cord
tun
hogshead
gill
dram
cc
peck
hobbit
stack
omer
wey
The most famous error involving units was the crash of a satellite intended for studying the climate on Mars. Standard and metric units got mixed up and hundreds of millions of dollars worth of scientific tools were burned up in the atmosphere.
Measure Time
Measure your left foot in Centimeters.
Analysis
Find the average foot (in cm) for each of our 3 sections.
Fundamental Units
Length Unit: meter,
m, the distance traveled by light in a vacuum during a set time
Mass Unit: the kilogram,
kg, based on a specific Pt-Ir cylinder kept at the International Bureau of Standards Updated in 2019!
Time Unit: seconds,
s, based on the frequency of radiation from a cesium atom
Length Scales
Derived Units
Often, we'll combine 2 or more of the fundamental, or base, units to create a
derived unit. This might be something like
miles per hour, or
PSI (pounds per square inch), or density: $$\rho = \frac{kg}{m^3} = \frac{m}{V}$$
Dimensions
Dimension has a specific meaning – it denotes the physical nature of a quantity. Some quantity is either a length, or a time, or a mass, or some combination of these.
Dimensions are denoted with square brackets, for example:
To analyze the dimensions of this, we would write:
$$[L] = \left[\frac{L}{T}\right] \times [T]$$
Notice how the dimensions of both sides match. [L]
Unit Conversion
We have to be able to convert between different units. For example, as you drive from the US in to Canada, the speed limit signs change from miles per hour (mph) into kilometers per hour (kph). In many of our physics problems, we'll use meters per second.
Example:
Convert 55 miles per hour into meters per second.
Example:
Convert 20 square meters into square feet
Example:
Convert 500 pounds per cubic yard into SI units
Take a guess as to which cube would represent the volume of Vaccine needed to give every New Yorker 2 doses.
How many liters of vaccine would NYC need to inoculate all 8 million residents, assuming each person receives two doses of 0.5 cc each.
How many gallons would this be?
An average household freezer is about 10 cubic feet in volume. How many freezers would be needed to store all this vaccine (assuming there was no space devoted to packaging)?
How do you know which units to use?
Use the context of the situation to guide you.
Also: who's your audience?
Notations
Some quantities have one symbol used consistently
e.g. for time,
t is used
Some quantities have many symbols used:
e.g. lengths may be
x, y, z, r, d, h, etc.
Just be consistent!
Scientific Notation and the metric prefixes
Metric prefixes in everyday use
Text
Symbol
Factor
tera
T
1000000000000
giga
G
1000000000
mega
M
1000000
kilo
k
1000
hecto
h
100
(none)
(none)
1
deci
d
0.1
centi
c
0.01
milli
m
0.001
micro
μ
0.000001
nano
n
0.000000001
pico
p
0.000000000001
Significant Figures/Uncertainty/Measurements
This is NIST: Precision Measurements Lab.
Let them handle 10 decimal places.
Orders of Magnitude
Physicists love doing this: estimate to within 1 power of ten of some quantity from the world. For example:
Distance to the Sun: $10^{11}$ m
Length of a fly: $10^{-3}$m
Mass of a page from the textbook: $10^{-2}$ kg
Estimate the circumference of the earth if it's 4000 km between NY and LA