d. roberts phys 121 university of maryland phys 121: fundamentals of physics i september 6, 2006
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![Page 1: D. Roberts PHYS 121 University of Maryland PHYS 121: Fundamentals of Physics I September 6, 2006](https://reader036.vdocuments.net/reader036/viewer/2022082516/56649d3e5503460f94a16d53/html5/thumbnails/1.jpg)
PHYS 121University of MarylandD. Roberts
PHYS 121:PHYS 121:Fundamentals of Fundamentals of
Physics IPhysics ISeptember 6, 2006
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PHYS 121University of MarylandD. Roberts
Reminders & AnnouncementsReminders & Announcements
• I would like to start using clickers this week. Your clicker should look like this:– You will need to register your clicker:
• http://www.clickers.umd.edu/
• First homework on WebAssign, due Sunday at midnight
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PHYS 121University of MarylandD. Roberts
OutlineOutline
• Clicker setup
• Measurement– Units– Dimensional Analysis
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PHYS 121University of MarylandD. Roberts
Clicker SetupClicker Setup
• The clicker channel for this lecture hall will be
• To set the channel on your clicker:– Press “GO”
• Light should blink red/green
– Enter 2-digit channel number (50)– (Newer clickers only) Press “GO” again– Light should turn solid green for a few seconds
50
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?In January, the days get:In January, the days get:
0% 0%0%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
1. Longer
2. Shorter
3. Stay the same
?
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PHYS 121University of MarylandD. Roberts
Measured quantitiesMeasured quantities
• A measured quantity can be treated as if it is the algebraic product of these three items.
h 1
m 60h 61h 6
h 1
m 601m 60h 1
h 6
t
t
m 360
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PHYS 121University of MarylandD. Roberts
What have we learned?What have we learned?
• A physics equation is not just numbers.• This equation is OK: 1 inch = 2.54 cm• So is this: 1 = (2.54 cm)/(1 inch)• It says: 1 = L1 / L2
which means these two lengths are the sameno matter how we measure them.
• We can treat units as if they are algebraic symbols, multiplying them, canceling them, etc.
in 63360ft mi
inft mi1252801
ft 1
in 12
mi 1
ft 5280mi 1 mi 1
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PHYS 121University of MarylandD. Roberts
UnitsUnits
• A unit is– the specific choice of arbitrary scale we make to measure a
particular quantity that has a particular dimension.
• We can choose to measure “length” in– meters– centimeters– inches– yards– furlongs– light-years
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PHYS 121University of MarylandD. Roberts
Accuracy and PrecisionAccuracy and Precision
• No measurement in science is ever perfect.• A critical element in measurement is
understanding how well you know it.• Accuracy means how “correct”
the measurement is.• Precision means how many significant figures
you have.
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PHYS 121University of MarylandD. Roberts
Some QuestionsSome Questions
• Which is better?– A measurement of high accuracy and low precision?– A measurement of low accuracy and high precision?
• Which statement is precise? Which is accurate?– The earth is a sphere.– There is a point in the center of the earth such that
if you measure the distance to the surface in any direction, you will get the same result to within 1%.
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PHYS 121University of MarylandD. Roberts
DimensionsDimensions
• For every new arbitrary scale we choose, we assign a dimension.– A dimension specifies the kind of measurement
(or combination of measurements) we are measuring to get the number.
• This term we introduce measurements of– length (L)– time (T)– mass (M)
• We write the dimensions of a combined quantity like this:
v = 6.5 m/s[v] = L/T
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PHYS 121University of MarylandD. Roberts
Careful!Careful!
• Dimensions are not algebraic symbols – they are type labels.
6 ft + 9 ft = 15 ft
[6 ft] + [9 ft] = [15 ft]
L + L = L (Not 2L !)• We sometimes use “L” (or “M” or “T”)
for algebraic symbols – to specify a particular length or mass or time. You have to know whether you are doing a dimensional analysis or a calculation!
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PHYS 121University of MarylandD. Roberts
Dimensional AnalysisDimensional Analysis
• Why do we care?• Since the measurement scale for a dimension
is arbitrary, we could change it.• A dimensional analysis tells us how a quantity changes
when the measurement scale is changed.• Any equation which is supposed to represent a physical
relation must retain its equality when we make a different choice of scale.
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PHYS 121University of MarylandD. Roberts
Letting dimensional analysis work for youLetting dimensional analysis work for you
• In physics, if we try to add or equate quantities of different dimensions we get nonsense.
• If we didn’t maintain dimensional correctness, an equality that worked in one measurement system wouldn’t work in another.
• This is a very good way to check your work with equations. (But it’s hard to do if you put numbers in too early!)
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? Which of these equations can represent Which of these equations can represent a physical equality?a physical equality?
3 m
eter
s =
3 se
conds
1 m
eter
= 1
met
er2
3 m
eter
s =
1 m
eter
+ ..
.
4 m
eter
s2 =
1 m
eter
2 ...
All
of them
None
of the
m
More
than
one
but not..
.
0% 0% 0% 0%0%0%
100%
41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
1. 3 meters = 3 seconds2. 1 meter = 1 meter2
3. 3 meters = 1 meter + 2 meter2
4. 4 meters2 = 1 meter2 + 3 meter2
5.5. All of themAll of them6.6. None of themNone of them7.7. More than one but not allMore than one but not all
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PHYS 121University of MarylandD. Roberts
Making Dimensions Work for YouMaking Dimensions Work for You
• Find the error in the following calculation by using dimensional analysis.
• [x] = L[v] = L/T[a] = L/T2
[t] = T• “” means “change in”
0
1 0 0
1 0
0
0
0
2
2
F
F
F
F
v a t
v v a t
v v v
vta
vx t
vx
a
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PHYS 121University of MarylandD. Roberts
What have we learned?What have we learned?
• In physics we have different kinds of quantities depending on how they were measured.
• These quantities change in different ways when you change your measuring units.
• Only quantities of the same type may be equated (or added) otherwise an equality for one person would not hold for another.
333 cm 5cm 4cm 1 )(anythings 5cm 4 cm 1 2