PHYS-211:
UNIVERSITY PHYSICS I
Dr. Vladimir Sobolev
Dr. Xinhua Bai
SDSMT
Chapter 1
Physics and Measurement
1.1 Physics
•  Physics & Experiments: Physics is an
experimental science, with a lot theoretical
and mathematical thinking.
•  Experiments: Measuring, providing
quantitative conclusions, not qualitative!
–  Distance: 10-32 m (elementary particles) ~ 10+53 m
(known universe)
–  Time: 10-23 s (life time of most unstable subatomic
particles) ~ 10+17 s (age of known universe)
1.2 More about Measuring things
•  Resolution:
–  A ± σ
Example: 5’10’’ ± 1’’ for your height
–  More interesting to experimental physicists than to most of
us.
•  Resolution depends on many things:
–  Equipment
–  Method being used
–  Analysis techniques: quantities that are not directly
measurable
–  People
1.2 More about Measuring things: Continued
•  Unit: We measure each quantity by its own
“unit” or by comparison with a standard.
A unit is a measure of a quantity that scientists
around the world can refer to.
This has to be both accessible and invariable.
For example
•  1 meter (m) is a unit of length. Any other length can
be expressed in terms of 1 meter. A variable length,
such as the length of a person’s nose is not
appropriate.
1.3 International System of Units
The SI system, or the International
System of Units, is also called the
metric system.
Three basic quantities for the study of
motion are the length, time, and mass.
Many units are derived from this set,
as in speed, which is distance divided
by time: They are called “derived
units”.
We will use them throughout this
course: Physics of motions!
Scientific notation
•  Scientific notation uses the power of 10.
• 
Easy for very big or very small numbers
Example:
3 560 000 000 g = 3.56 x 109 g (or 3.56E9 g. E: exponent of 10)
0.000 001 352 m-3 = 1.352 x 10-6 m-3 (or 1.352E-6 m-3)
• 
Easy for estimation of magnitude
Example:
3 560 000 000 g / 0.000 001 352 m-3 = ???
3.56 x 109 g / 1.352 x 10-6 m-3 = (3.56 / 1.352) x (109 /10-6 ) (g / m-3 )
~ 2.6 x 1015 g/m-3 .
• 
Significant digits – related to error
1000 à 3, 1000.0 à 5, 1000. à 4
3.14159 à 6, 0.00035 à 2, 0.0350 à 3
•  Sometimes special names are used to describe very large or very small
quantities (as shown in Table 1-2).
For example, 2.35 x 10-9 = 2.35 nanoseconds (ns)
Special Names of Big Numbers
1.4 Changing units
Based of the base units, we may need to change the units of a
given quantity using the chain-link conversion.
For example, since there are 60 seconds in one minute,
1 min
60 s
=1=
, and
60s
1 min
60 s
2 min = (2 min) x (1) = (2 min) x (
) = 120 s
1 min
Conversion between one system of units and another can
therefore be easily figured out as shown.
The first equation above is often called the “Conversion
Factor”.
1.4 Changing units: Continued
Sometimes it may be trickier:
1. Temperature: Celsius, Fahrenheit, Kelvin (SI, absolute temperature)
9
F = C • + 32
5
5
C = (F − 32) = (F − 32) /1.8
9
K = C + 273
2. Derived quantities: Speed for example
mile
m
=?
hour
s
mile
1609.34m
m
1
=1
= 0.44
hour
3600s
s
1
1.5 Length
Understanding the “meter”: Historic definitions
1792: the meter was defined as one-millionth the distance from the north
pole to the equator.
Later: the meter was defined as the distance between two finely engraved
lines near the ends of a standard Platinum-Iridium bar, the standard meter
bar. This bar is placed in the International Bureau of Weights and
Measures near Paris, France.
1.5 Length
Modern definitions:
1893: The standard metre was first measured
with an interferometer by Albert A. Michelson,
the inventor of the device and an advocate of
using some particular wavelength of light as a
standard of length.
1960: the meter was defined to be 1 650 763.73 wavelengths of a particular
orange-red light emitted by krypton-86 in a discharge tube that can be set
anywhere in the world.
1983: the meter was defined as the length of the path traveled by light in a
vacuum during the time interval of 1/299 792 458 of a second. The speed
of light is then exactly 299 792 458 m/s. c = constant!
We are getting more and more precise with new techniques
1.5 Length (Continued)
Some examples of lengths
Standard candle, Hubble’s Law
Rulers,
laser,
radar ranging,
star parallax
Particle scattering, accelerators
They rely on different techniques!
Cosmological Distance
ly: light year, the distance that light travels in one year.
1 ly ~ 300,000,000 m/s × 365 d × 24 h/d × 3,600 s/h
~ 3 × 108 × 3.65 × 102 × 2.4 × 101 × 3.6 × 103 m
~ 95 × 1014 m ~ 9.5 × 1015 m
1.5 Length: Estimation
The world’s largest ball of
string is about 2 m in radius. To the
nearest order of magnitude, what is
the total length, L, of the string of
the ball?
PROBLEM:
The Big Picture for Understanding:
1.  Assume that the ball is a sphere of radius 2 m. In order to get a
simple estimate, assume that the cross section of the string is a
square with a side edge of 4 mm. This overestimate will
account for the loosely packed string with air gaps.
2.  Units: m and mm
Length: 1 mm = 10-3 m
Area: 1 mm2 = (10-3 m) × (10-3 m) = 10-6 m2
1.5 Length: Estimation
The total volume of the string is roughly the volume
of the sphere. Therefore,
CALCULATE:
Volume of the string: area ×length
Volume of a ball
4
V = (4 ×10 m) × L = π R 3 ≈ 4R 3
3
R = 2m
−3
2
4(2 m)3
4 × 8 m3
6
⇒L=
=
=
2×10
m
−3
2
−6
2
(4 ×10 m) 16 ×10 m
1.6 Time: What is it?
Time: A major subject of study in religion, philosophy and science, with
two contrasting viewpoints on time:
(1)  Time is part of the fundamental structure of the universe, like some
kind of "container" that events and objects "move through", or some
entity that "flows”.
(2)  Part of a fundamental intellectual structure (together with space and
number) within which humans sequence and compare events. It is
neither an event nor a thing, and thus is not itself measurable nor can
it be travelled.
(3) Modern physics: Time is relative – moving clock is slower!
Time: What is it?
In this course, time can be understood as:
1: A dimension in which events can be ordered from the past through the
present into the future. à Your height H(t), your weight W(t), your
homework load HW(t), ….
or
2: The measure of durations of events and the intervals between them. à
PHYS-211 class ~ 50 min, our lifetime ~ 70 years, …
How to measure time? From various “periodic” motions to atomic clocks
Clock is a device that can “repeat its behavior” periodically
hourglass sundial mechanical clock
How precisely it can repeat its behavior determines its precision.
Atomic clock
An atomic clock: It uses an electronic transition
frequency in the microwave, optical, or ultraviolet
region of the electromagnetic spectrum of atoms as
a frequency standard for its timekeeping element.
Atomic clocks give very precise time
measurements: Accurate to seconds in
many millions of years!
An atomic clock at the National Institute of Standards
and Technology in Boulder, CO, is the standard, and
signals are available by shortwave radio stations.
In 1967 the standard second was defined to be the
time taken by 9 192 631 770 oscillations of the light
emitted by Cesium-133 atom.
NIST-F1, source of the
official time of the US
Time in the world
1.7 Mass: Another concept that sounds simple but indeed very
complicated
•  Simplest definition: The amount of matter in certain types of samples.
•  The concept distinguishes conceptually when we talk about different
effects:
•  Motion à Inertial mass, F=ma
This course
•  Interactions à Gravitational mass, F=Gm1m2/r2
•  Energy à E=mc2
•  Space-time à Curvature
How to measure mass
A platinum-iridium cylinder, kept at the
International Bureau of Weights and
Measures near Paris, France, has the
standard mass of 1 kg.
Another unit of mass is used for atomic mass measurements. Carbon-12
atom has a mass of 12 atomic mass units, defined as
1u = 1.660 53886 x 10 −27 kg
In particle physics, mass is often measured in units of eV/c2
– (electron Volts)/(speed of light)2
– Thanks to Albert Einstein E=mc2 and C is a constant!
1eV = 1. 602 ×10 −19 J
1eV / c 2 = 1.782 ×10 −36 kg
Mass in the world
mp= 938.272 MeV/c2
= 1.0073 u
me= 0.511 MeV/c2
= 5.486 ×10-4 u
Mass and Weight
What is the difference between mass and weight?
•  How do we measure them?
•  Balance scale
•  Spring scale
•  Units of them?
•  g, kg, …
•  Newton (force!), Often by pound, kg
•  How do they change?
•  At different locations
•  At different speed
•  Precise definitions in physics:
•  Mass is a quantitative measure of an object's resistance to
acceleration (inertial mass). Or a measure of magnitude of the
gravitational force (gravitational mass).
•  Weight is the gravitational force acting on a given body.
1.8 Density
Density is typically expressed in kg/m3, and is often expressed as the
Greek letter, Rho (ρ).
Example, Density and Liquefaction:
Grains and Voids
Grain density (SiO2)
Sand density
Voids
V=Vsands+Vvoids
Density: Continued
Density: Continued
m
density =
V