Note: course website is
http://mail.sci.ccny.cuny.edu/~jtu/Teaching.htm
PHYS-207 for Scientists
Lecture 1: Measurements and Units
HW1 (problems): 1.18, 1.27, 2.11,
2.17, 2.21, 2.35, 2.51, 2.67
Due Friday, Feb. 6.
Note: course website is
http://mail.sci.ccny.cuny.edu/~jtu/Teaching.htm
PHYS-207 for Scientists
Section PP: Honors
Instructor:
Professor Jiufeng J. Tu
Office:
MR-330A Marshak
Office Hours: Tuesdays, 11:00-2:00 pm
E-Mail:
jtu@sci.ccny.cuny.edu
Requirements

Book: Fundamentals of Physics (9th ed.) by Halliday & Resnick,
and Walker.

Lectures:
417A
9:30 – 10:50 on Tues, Thurs and Fridays in MR-
Note: course website is
http://mail.sci.ccny.cuny.edu/~jtu/Teaching.htm

Labs and Recitations: Fridays, 2:00 – 3:50 in MR-409s (starting
on Feb. 6). You have to pass the lab requirements to pass this
course. Take the labs (7 in total) seriously since questions on the
lab materials will also be in the tests. The Physics Department Lab
manual is available on line at
http://www.ccny.cuny.edu/physics/introlabman.cfm.
Grading Scheme

This is how your final grade will be determined:
Homework: (~12 of them): 10%
Lab Reports: (7 of them): 10%
Midterms: (two): 40%
Final: 40%

Labs: (7) You have to pass the lab requirements
to pass this course. Take them serious!
Course Scope: Mechanics
Kinematics → Dynamics → Thermodynamics
1.2 Measuring things
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 are the
length, time, and mass.
Many units are derived from
this set, as in speed, which is
distance divided by time.
US Customary System

Still used in the US, but text will use SI
Quantity
Unit
Length
foot
Mass
slug
Time
second
Prefixes



Prefixes correspond to powers of 10
Each prefix has a specific name
Each prefix has a specific abbreviation
1.3 International System of Units
Scientific notation uses
the power of 10.
Example:
3 560 000 000 m = 3.56
x 109 m.
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 s = 2.35
nanoseconds (ns)
Basic Quantities and Their
Dimension


Dimension has a specific meaning – it
denotes the physical nature of a quantity
Dimensions are denoted with square
brackets



Length [L]
Mass [M]
Time [T]
Dimensions and Units


Each dimension can have many actual units
Table for the dimensions and units of some derived
quantities
Dimensional Analysis


Technique to check the correctness of an equation
or to assist in deriving an equation
Dimensions (length, mass, time, combinations) can
be treated as algebraic quantities




add, subtract, multiply, divide
Both sides of equation must have the same
dimensions
Any relationship can be correct only if the
dimensions on both sides of the equation are the
same
Cannot give numerical factors: this is its limitation
Symbols


The symbol used in an equation is not necessarily
the symbol used for its dimension
Some quantities have one symbol used consistently


For example, time is t virtually all the time
Some quantities have many symbols used,
depending upon the specific situation

For example, lengths may be x, y, z, r, d, h, etc.
Conversion of Units

When units are not consistent, you may need
to convert to appropriate ones

Units can be treated like algebraic quantities
that can cancel each other out
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”.
1.5 Length
Redefining the meter:
In 1792 the unit of length, 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.
In 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.
In 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.
1.5 Length
Some examples of lengths
Reasonableness of Results


When solving a problem, you need to check
your answer to see if it seems reasonable
Reviewing the tables of approximate values
for length, mass, and time will help you test
for reasonableness
1.5 Time
Atomic clocks give very
precise time
measurements.
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.
1.5 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. Carbon12 atom has a mass of
12 atomic mass units,
defined as
1u  1.66053886 x 1027 kg
Standard Kilogram
1.5 Density
Density is typically expressed in
kg/m3, and is often expressed as
the Greek letter, rho (r).
Example, Density and Liquefaction:
Uncertainty in Measurements

There is uncertainty in every measurement –
this uncertainty carries over through the
calculations



May be due to the apparatus, the experimenter,
and/or the number of measurements made
Need a technique to account for this uncertainty
We will use rules for significant figures to
approximate the uncertainty in results of
calculations
Significant Figures


A significant figure is one that is reliably known
Zeros may or may not be significant



Those used to position the decimal point are not significant
To remove ambiguity, use scientific notation
In a measurement, the significant figures include the
first estimated digit
Significant Figures, examples

0.0075 m has 2 significant figures



10.0 m has 3 significant figures


The leading zeros are placeholders only
Can write in scientific notation to show more clearly:
7.5 x 10-3 m for 2 significant figures
The decimal point gives information about the reliability of
the measurement
1500 m is ambiguous



Use 1.5 x 103 m for 2 significant figures
Use 1.50 x 103 m for 3 significant figures
Use 1.500 x 103 m for 4 significant figures
Note: course website is
http://mail.sci.ccny.cuny.edu/~jtu/Teaching.htm
PHYS-207 for Scientists
Lecture 1: Measurements and Units
HW1 (problems): 1.18, 1.27, 2.11,
2.17, 2.21, 2.35, 2.51, 2.67
Due Friday, Feb. 6.