D. Roberts PHYS 121 University of Maryland PHYS 121: Fundamentals of Physics I September 6, 2006

PHYS 121University of MarylandD. Roberts

PHYS 121:PHYS 121:Fundamentals of Fundamentals of

Physics IPhysics ISeptember 6, 2006


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


OutlineOutline

• Clicker setup

• Measurement– Units– Dimensional Analysis


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

?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

?


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


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


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


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.


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%.


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


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!


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.


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!)

? 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


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


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

Documents

D. Roberts PHYS 121 University of Maryland PHYS 121: Fundamentals of Physics I September 6, 2006