Intro and Units

About physics

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
Fluids Condensed Matter
Waves Bio-Physics

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.

  1. Theories must be verifiable by experiment
  2. Phenomena can be described mathematically
  3. 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.


Find the average foot (in cm) for each of our 3 sections.

Fundamental Units

The Kilogram prototype

  • 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

Length Scales of Science

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: $$\rho = \frac{kg}{m^3} = \frac{m}{V}$$


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:

  • Length [L]
  • Mass [M]
  • Time [T]

Dimensional Analysis

Take our familiar velocity: say miles per hour.

$$\textrm{distance} = \textrm{velocity} \times \textrm{time}$$

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.


Convert 55 miles per hour into meters per second.


Convert 20 square meters into square feet


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?


  • 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

Other things to know:

  • Greek Alphabet
  • Algebra
  • Trigonometry
  • Calculus (slopes)
  • Calculus
  • Function Plotting