Physics 231
Topic 1: Introduction, Units, Significant Figures
Alex Brown
September 2, 2015
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Today's Lecture:
Key Concepts

Syllabus

International System of Units (SI)

Mass: kilograms (kg)

Length: meters (m)

Time: seconds (s)

Units and conversions

Dimensional Analysis

Scientific Notation (e.g., 4.3x1012 and 2.3E4)

Significant Figures
Covers chapter 1 in Rex & Wolfson
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Textbook & Reading
Essential College Physics, Volume 1
• The syllabus lists the relevant chapters for
each lecture and homework
• Read the material before class
• Not everything can be covered in class
• Lectures are not a replacement for the
textbook
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Homework
Homework is to be done online using LON-CAPA
http://msu.lon-capa.org
Homework assignments are due Tuesdays at 10 PM
The deadline is strict. Being away from a network connection is no excuse.
Do not wait until the last minute!
Assignments are somewhat unique to each student
Discussion board
You are encouraged to use the discussion board inside LON-CAPA. If you don't understand a problem, or you need
help, just click on the "Post Discussion" link and post your question. If you know the answer to somebody else's
question, don't be afraid to post you answer. Don't forget: The best way to learn is to teach.
But – to do well in the exams you should try the problem on your own first, and if you use the discussion board,
be sure you understand the concepts and the reasoning behind the solution.
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Extra Credit Quizzes
We will be doing in-class quizzes using i>Clickers
 Quizzes will be given almost everyday
You must have in i>Clicker to participate
Start to count them on Monday September 14th
Be on time, quizzes are sometimes at the beginning of class.
There are NO make-ups for quizzes all of the points are for extra credit
You must take quizzes in this section. No credit for quizzes in other sections.
Quiz points: 3 for correct answers, 1 for incorrect answers
Scores will be posted on my website occasionally – check to ensure you're registered
You must register your i<Clicker on lon-capa before Monday September 14th
 Even if you have registered before, you need to re-register for this course!
 You MUST enter the preceding “A” before your student ID
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Extra Credit Quizzes
You must use your own and ONLY your own
i>Clicker in class
 If you are found to be using another
person's i>Clicker, all clickers will be
confiscated
 This will be considered a violation of
the rules governing academic
dishonesty
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Information and links
Lecture ppt and pdf
Grade updates
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Physics Learning Center (PLC)
The Strosacker Physics Learning Center is located in BPS 1248
 Details and schedule TBA
 The PLC is a cooperative learning center, not a help room. TAs will
encourage group work and will help groups who get stuck.
 Group work
 A very effective learning tool for both strong and weak students
 You must do your own assignments and must learn how to do problems on
your own
 Do as much as you can of the assignments before group work – PREPARE!
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How to Suceed in PHY231



Read the book before coming to class.
Go to the Physics Learning Center frequently! The TAs are there to help you learn.
Always attend the lectures.
 Recognize that learning physics is different than many other subjects
 Physics is about understanding concepts and connecting your knowledge with
these concepts. Physics is not just about memorizing facts.
 Some physics concepts will be contrary to your instincts, but not contrary to
your intellect. Be willing to think things through!
 Keep working continuously – do the reading assignments, think about what you
learned in lecture, keep thinking AS WE GO. Memorizing facts is not sufficient,
so cramming before an exam is not effective.
 Understanding the concepts helps you set up solutions to problems. Equation
hunting is not a good strategy.
 Little is learned by copying or memorizing the solution of another student.
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DOs and DON'Ts
DON'T...
 ...use LON-CAPA postings from others before you have given a problem a genuine
attempt yourself. If you have to frequently look at how others solved the problem, it
means you aren't understanding the material well.
 ...try to memorize LON-CAPA problems; it is unlikely that you will get many
problems in exams that are exactly like the homework
 ...base your entire study routine on LON-CAPA. Bring variation in your studies and
practice questions that are not phrased like LON-CAPA (eg, questions in the book)
 ...wait until the last weeks of the semester to ask for help if you need it (ie, if you're
working hard but still are not doing well)
 ...cheat on exams, quizzes, homework
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DOs and DON'Ts
DON'T...
 …use your cell phone in class.
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Why Learn Physics?
Example:
Tacoma Narrows Bridge
Golden
Gate
BronxWhiteStone
Tacoma
Narrows
Year
1937
1939
1940
Cost
$35M
$20M
$6.4M
Length
4200 ft
2300 ft
2800 ft
Width
90 ft
74 ft
39 ft
Ratio:
Width to
Length
1 : 47
1 : 31
1 : 72
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Why Learn Physics?
Example: Mechanics of the Skeleton
Key concept for:
• Human medicine
• Veterinary medicine
• Sports training
• Ergonomic engineering
In other classes, you learn the names
of bones, how to treat broken bones,
where to drill to replace things.
Physics teaches you HOW and WHY it works
(and how to understand the system as a whole)
 Combination is the key to innovation!
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Why Learn Physics?
Example: Dark Matter & Dark Energy
Bullet Cluster
• Cosmological measurements have told
us that our universe is not made the
way we thought.
• IE, what we see in telescopes
corresponds to what we are all made
out of: atoms (stars, gases, planets)
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Why Learn Physics?
Example: Dark Matter & Dark Energy
• Cosmological measurements have told
us that our universe is not made the
way we thought.
Bullet Cluster
• IE, what we see in telescopes
corresponds to what we are all made
out of: atoms (stars, gases, planets)
• But this is only 4% of what’s out there!
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Système Internationale (SI) Units
(ones used for this course)
Unit
meter
kilogram
second
Kelvin
mole
(others)
ampere
candela
Abbreviation
m
kg
s
K
mol
A
cd
Base unit for
length
mass
time
temperature
amount of substance
electric current
luminous intensity
 Also called the MKS unit system
 Based on powers of 10 relative to base units
 All other units derive from these (Area: m2, Speed: m/s, etc)
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Defining Standard Units
Original definition of the meter: 1/10,000,000 of earth's arc length
 Today: 1m = distance light travels in 1/299,272,458 s
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Defining Standard Units
Platinum-Iridium
Kilogram Prototype
 The kilogram defined by a fixed “prototype” of matter
Standards are important: when you buy 1kg of gold, you want to get it right!
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Defining Standard Units
Cesium Atomic Clock
National Institute of
Standards and Technology
(NIST)
Original definition of the second: 1/86,400 of a solar day
 1960: based on a tropical year
 Since 1967: 9,192,631,770 periods of radiation corresponding to the transition
between two hyperfine states of the ground state of 133Cesium
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Unit Conversion Example
Treat conversions as algebraic equivalencies:
Convert by multiplying your existing units by a numerical equivalent of 1.0
Jon has walked 3 miles in 1 hour, what is his average speed in m/s?
Given: 1 mile = 1609.3 m
ie, 1.0 = ( 1609.3 m/ 1 mile )
Velocity (speed) = distance / time
= ( 3 miles ) / ( 1 hour )
Equal to 1.0
= ( 3 miles/hr ) x ( 1609.3 m / mile )
= 4827.9 m/hr
= ( 4827.9 m/hr ) x (1 hr / 60 min) x (1 min / 60 sec)
= ( 4827.9 m/hr ) x (1 hr / 3600 s)
= ( 4827.9/3600 ) m/s
= 1.341 m/s
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A Wide Range of Units
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Very Large and Very Small Numbers
0.000000000000001 = 10-15 = 1E-15 femto (f)
0.000000000001
= 10-12 = 1E-12 pico (p)
0.000000001
= 10-9 = 1E-9 nano (n)
0.000001
= 10-6 = 1E-6 micro ()
0.001
= 10-3 = 1E-3 milli (m)
0.01
= 10-2 = 1E-2 centi (c)
0.1
= 10-1 = 1E-1 deci (d)
1
= 100 = 1E+0
10
= 101 = 1E+1 deca (da)
100
= 102 = 1E+2 hecto (h)
1000
= 103 = 1E+3 kilo (k)
1000000
= 106 = 1E+6 mega (M)
1000000000
= 109 = 1E+9 giga (G)
10000000000
= 1012 = 1E+12 tera (T)
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Scientific Notation
 For very large or very small numbers the scientific notation is
advantageous.
 Write number as mantissa x 10Exponent
 Example:
0.000000001 = 1 × 10-9
34000000 = 3.4 × 107
 Alternative notation: 3.4E7 (CAPA, computers)
1 m = 1000 mm = 1E3 mm
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Significant Figures
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Significant Figures
Two statements:
 The population of the USA is 294,109,799
 The population of the USA is 294,000,000=2.94×108
 First statement implies precision that is probably not warranted
 Second statement claims that the population is somewhere between 293M
and 295M. This is reasonable!
General Rules:
 The number of digits we write down in a number specifies the precision with
which we can claim to know the number
 All non-zero figures are signficant (except exponent in scientific notation)
 Zeros only count when
They are between non-zero figures
They are to the right of a non-zero figure and there is a decimal point
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Significant Figures Example
An athlete must bicycle around a circular track for a
time trial. His coach tells him that the radius of the
circular track is 40.2 m. How far does he ride?
Formulae: C = π D = 2 π R
D = diameter of the circle
R = radius of the circle
π = 3.14159265.....
We know π to many decimal places, but we only
know the radius is between 40.2 and 40.3 m (ie,
3 significant figures).
Thus we can only know the circumference to
3 significant figures! What is the answer?
C = 2 × 3.14159265... × 40.2 m = 253 m
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How to Solve Problems
There are no general rules but here are some pointers:
1) READ the problem carefully!
2) Summarize (throw away unnecessary info)
3) Visualize (drawing can often help)
4) Convert units (consistency)
5) Set up equations:
Plug in numbers if not comfortable with solving sets of equations
If confident, plug in numbers at last moment
6) Check whether answers (and units) make sense
7) In exams: once you have solved a problem, check calculations one
more time at the end of exam. Especially important if you tend to
make small mistakes
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Greek Alphabet
We will use some of those…
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2D Geometrical Objects
object
surface
circumference
square
Length2
4xlength
triangle
½x base x height Side1+side2+side3
circle
x radius2
2 x  x radius
Radius=diameter/2
rectangle
Length x height
2xlength +
2xheight
oval
xr1xr2
-
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3D Geometrical Objects
object
surface
volume
6xlength2
length3
2hw+2lh+2wh
hlw
sphere
4r2
(4/3) x r3
cylinder
2rh
r2h
cube
rectangle
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Solving Quadratic Equations
ax 2  bx  c  0
a0
 b  b 2  4ac
x
2a
In general there are 2 solutions. In physics problems,
One of them is usually not realistic and is thrown out.
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Calculate the length of the shorter of two sides of a
rectangle, which has an area of A = 24 m2 and a perimeter
of p = 22 m. Example of two equations and two unknowns.
h
A = wh
p = 2w+2h
24 = wh so w = 24/h
22 = 2w + 2h = (2x24/h) + 2h = (48/h) + 2h
w
-2h2 + 22h - 48 = 0
 22  22  4(2)( 48)  22  10
h

2(2)
4
h  8 or 3
w  3 or 8
2
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ax 2  bx  c  0
a0
 b  b 2  4ac
x
2a
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Dimensional Analysis
Dimensions should be treated as algebraic quantities
 If you know the dimensions you want in the end of a calculation, it helps you plan
your work and check your math
Example:
 Calculate the distance traveled in 10 seconds by an object starting at rest and
traveling at constant acceleration
 Given : x = (1/2) a t2
 What are the units for a (acceleration)?
Rearrange to get units for a:
[?] = [m] / [s2] )= m/s2
[m] = [?]  [s2]
Units of acceleration go here
Check your math: [m] = [m/s2]  [s2] = [m]
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