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AP Physics Chapter 1
Measurement
1
AP Physics
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Lecture
Q&A
Website: http://www.mrlee.altervista.org
Measurement and Units
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Physics is based on measurement.
International System of Units (SI unit)
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Created by French scientists in 1795.
Two kinds of quantities:
–
Fundamental (base)quantities: more intuitive

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Derived quantities: can be described using fundamental
quantities.
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3
length, time, mass …

Speed = length / time
Volume = length3
Density = mass / volume = mass / length3
Units
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Unit: a measure of the quantity that is defined
to be exactly 1.0.
Fundamental (base) Unit: unit associated with
a fundamental quantity
Derived (secondary) Unit: unit associated with
a derived quantity
–
4
Combination of fundamental units
Standard Units
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Standard Unit: a unit recognized and accepted by all.
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Standard: a reference to which all other examples of the
quantity are compared.
Standard and non-standard are separate from fundamental and
derived.
Some SI standard base units
Quantity
Unit Name
Unit Symbol
Length
Meter
m
Time
Mass
Second
kilogram
s
kg
Length
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Standard unit: meter (m)
Standard meter bar: International Bureau of Weights
and Measures near Paris
Secondary standards: duplicates
In 1983:
The meter is the length of the path traveled by light in
vacuum during a time interval of 1/299,792,458 of a
second.
Other (nonstandard) units: cm, km, ft, mile, …
Time



7
Standard unit: second (s)
One second is the time taken by 9,192,631,770
vibrations of the light (of a specified
wavelength) emitted by a cesium-133 atom.
Other nonstandard units: min, hr, day, …
Mass


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Standard unit: kilogram (kg)
Standard kilogram cylinder: International
Bureau of Weights and Measures near Paris
Other nonstandard units: g, Lb, ounce, ton, ..

Atomic mass unit (amu, u)
1 u = 1.6605402  10-27 kg
8
Changing Unit: Conversion Factors

Conversion factor: a ratio of units that is equal to one.
1 min
1min  60s 
 1 and
60 s
So two conversion factors:
1 min
60 s
9
and
60s
1 min
60 s
1
1 min
A few equalities (conversion Factors) to
remember
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10
1 m = 100 cm
1 inch = 2.54 cm
1 mile = 1.6 km
1 hr = 60 min
1 min = 60 s
1 hr = 3600 s
Question?
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Two conversion factors from each identity, but
which one to use?
Depends on the unit we want to cancel.
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If the unit we want to cancel is on the top with the
numerator, then for the conversion factor we must
put that unit at the bottom with the denominator.
If the unit we want to cancel is at the bottom with the
denominator, then for the conversion factor we must
put that unit on the top with the numerator.
Example: 5 min = ___ s
1min  60s
 min 
5min  5min1  5min
 Does not work!
 60s 
min cannot be cancelled out. Not
good conversion factor.
 60 s 
5min  5min 
  300s
 min 
Good conversion factor.
12
1m  100cm
Practice:

Convert 12.3 m to cm
100cm
12.3m  12.3m 
 1230cm
1m
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Chain-link Conversion
Convert: 2 hr = ____ s
60 min 60 s  7200s

2hr  2hr 
min
hr
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1hr  60min
1min  60s
Practice:

1m  100cm
1inch  2.54cm
12 m = ___ inch
100cm
inch
12m  12m 

 472inch
1m
2.54cm
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1mile  1600m
1hr  3600s
Still simple? How about…
2 mile/hr = __ m/s
mile
mile  1600m 
2
2
 


hr
hr
 mile 
Chain Conversion
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 1hr   0.89 m


s
3600
s


1inch  2.54cm
More practice:
5 inch2 = _____ cm2
 2.54cm   2.54cm 
2
2
5inch 2  5inch  inch  
 
  32.258cm  32.cm
 inch   inch 
 2.54cm 
2
2
5inch  5inch  

 inch 
17
2
 32.cm2
When reading the scale,
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Estimate to 1/10th of the smallest division
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Draw mental 1/10 divisions
However, if smallest division is already too small,
just estimate to closest smallest division.
6
.5
7 cm
6.3 cm
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Uncertainty of Measurement
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All measurements are subject to uncertainties.
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External influences: temperature, magnetic field
Parallax: the apparent shift in the position of an
object when viewed from various angles.
Uncertainties in measurement cannot be avoided,
although we can make it very small.
Uncertainties are not mistakes; mistakes can be
avoided.
Uncertainty  experimental error
Precision
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Precision: the degree of exactness to which a
measurement can be reproduced.
The precision of an instrument is limited by the smallest
division on the measurement scale.
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–
Uncertainty is one-tenth of the smallest division.
Last digit of measurement is uncertain, the measurement
can be anywhere within ± one increment of last digit.
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Meter stick: smallest division = 1 mm = 0.001 m
uncertainty is 0.0001 m
1.2345m: 1.2344m -1.2346m
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4 digits after
decimal pt
3 digits after
decimal pt
Uncertainty and Precision
What
is the uncertainty of the meterstick?
0.0001m
 estimate
What is the precision of the meterstick?
 certain
0.001m
How
precise is the meterstick?
 certain
0.001m
Sometimes, when not strictly:
precision = uncertainty
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Both the uncertainty and precision of a meterstick is 0.0001m
Uncertainty and Precision
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What is the uncertainty and precision of 1.234?
Uncertainty = 0.001
Precision = 0.01 or 0.001 (loosely)
More precise = smaller uncertainty

Which is more precise, 12.34 or 2.345?
12.34: uncertainty = 0.01
2.345: uncertainty = 0.001
So, 2.345 is more precise.
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Accuracy
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
Accuracy: how well the result agrees with an accepted
or true value
Accuracy and Precision are two separate issues.
Example
Accepted (true) value is 1.00 m. Measurement #1 is
1.01 m, and Measurement #2 is 1.200 m.
Which one is more accurate? #1, closer to true value.
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Which one is more precise? #2, precise to 0.001m,
compared to 0.01m of #1
Significant Figures (Digits)
1. Nonzero digits are always significant.
2. The final zero is significant when there is a decimal
point.
3. Zeros between two other significant digits are always
significant.
4. Zeros used solely for spacing the decimal point are not
significant.
Example:
 1.002300  7 sig. fig’s

25
0.004005600  7 sig. fig’s

12300  3 sig. fig’s
Practice:
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How many significant figures are there in
a)
b)
c)
d)
e)
f)
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123000
1.23000
0.001230
0.0120020
1.0
0.10
3
6
4
6
2
2
Operation with measurements
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In general, no final result should be “more
precise” than the original data from which it
was derived.
Too vague.
Addition and subtraction with Sig. Figs
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The sum or difference of two measurements is
only as precise as the least precise one.
Example:
16.26 + 4.2 = 20.46 =20.5
 Which number is least precise?  4.2
 Precise to how many digits after the decimal pt?  1
 So the final answer should be rounded-off (up or
1
down) to how many digits after the decimal pt?
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Practice:
1)
2)
3)
4)
1)
2)
3)
4)
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23.109 + 2.13 = ____
12.7 + 3.31 = ____
12.7 + 3.35 = ____
12. + 3.3= ____
23.109 + 2.13 = 25.239 = 25.24
12.7+3.31 = 16.01 = 16.0
12.7+3.35 = 16.05 = 16.1
12. + 3.3 = 15.3 = 15.
Must keep this 0.
Keep the decimal pt.
Multiplication and Division with Sig.
Figs
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The number of significant digits in a product or quotient
is the number in the measurement with the least
number of significant digits
Example:
2.33  5.5 = 12.815 =13.
 Which number has the least number of sig. figs?  5.5
 How many sig figs?
 So the final answer should be rounded-off (up
or down) to how many sig figs?
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2
2
Practice:

2.33/3.0 = ___
2.33 / 3.0 = 0.7766667 = 0.78
2 sig figs
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2 sig figs
What about exact numbers?
Exact numbers have infinite number of sig. figs.
If 2 is an exact number, then 2.33 / 2 = __
2.33 / 2 = 1.165 = 1.17
Note:
 2.33 has the least number of sig. figs: 3
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Prefixes Used with SI Units
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Prefix
nano
micro
Symbol
n

Fractions
× 10-9
× 10-6
milli
centi
kilo
m
c
k
× 10-3
× 10-2
× 103
mega
giga
M
G
× 106
× 109
1 m = 1 × 10-6 m
1 mm = 1 × 10-3 m
Dimensional Analysis

[x] = dimension of quantity x
What is the dimension of K if
1 2
mv
2
?
Ignore
1 2
K  mv
2
  K    m v 
2
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K
2
length 
length 2
ML2

 mass 
or
  mass 
2
time
T2
 time 
When angle in unit of radian

r
l
l

r
 radian  180o
1o  60 '
1'  60"
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HW 57
1 AU
1”
1AU  92.9 10 miles
6
1 pc
 rad  180o 
1  60 '
o
1'  60"
1AU



1"

x
rad

1 pc


 1AU  x rad 1 pc  x pc
1 ly = distance traveled by light in one year
 speed  time
mile
 186, 000
1 yr
s
mile
 186, 000
y s
s
Convert 1 yr  y s
Conversion factor to convert
1AU  92.9 106 miles
36
 ly