1. AP Physics Chapter 1
Measurement

2. AP Physics Turn in Contract/Signature Lecture Q&A
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3. Measurement and Units Physics is based on measurement.
International System of Units (SI unit)
Created by French scientists in 1795.
Two kinds of quantities:
Fundamental (base)quantities: more intuitive
length, time, mass …
Derived quantities: can be described using fundamental quantities.
Speed = length / time
Volume = length3
Density = mass / volume = mass / length3

4. Units
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
Combination of fundamental units

5. Standard Units Standard Unit: a unit recognized and accepted by all.
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
Second s
Mass
kilogram kg

6. Length 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, …

7. Time 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, …

8. Mass 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 =  kg

9. Changing Unit: Conversion Factors
Conversion factor: a ratio of units that is equal to one.
and
So two conversion factors:
and

10. A few equalities (conversion Factors) to remember
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

11. Question?
Two conversion factors from each identity, but which one to use?
Depends on the unit we want to cancel.
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.

12. Example: 5 min = ___ s Does not work!
min cannot be cancelled out. Not good conversion factor.
Good conversion factor.

13. Practice:
Convert 12.3 m to cm

14. Chain-link Conversion
Convert: 2 hr = ____ s

15. Practice:
12 m = ___ inch

16. Still simple? How about…
2 mile/hr = __ m/s
Chain Conversion

17. More practice:
5 inch2 = _____ cm2

18. When reading the scale, Estimate to 1/10th of the smallest division
Draw mental 1/10 divisions
However, if smallest division is already too small, just estimate to closest smallest division. 6
7 cm .5
6.3 cm

19. Uncertainty of Measurement
All measurements are subject to uncertainties.
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

20. Precision
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.
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.
Meter stick: smallest division = 1 mm = m
uncertainty is m
3 digits after decimal pt
4 digits after decimal pt
1.2345m:
1.2344m m

21. Uncertainty and Precision
What is the uncertainty of the meterstick?
0.0001m
What is the precision of the meterstick?
0.001m
How precise is the meterstick?
 estimate
 certain
 certain
Sometimes, when not strictly:
precision = uncertainty
Both the uncertainty and precision of a meterstick is m

22. Uncertainty and Precision
What is the uncertainty and precision of 1.234?
Uncertainty = 0.001
Precision = 0.01
or (loosely)

23. More precise = smaller uncertainty
Which is more precise, or 2.345?
12.34: uncertainty = 0.01
2.345: uncertainty = 0.001
So, is more precise.

24. Accuracy
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 m.
Which one is more accurate?
#1, closer to true value.
Which one is more precise?
#2, precise to 0.001m, compared to 0.01m of #1

25. 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:
 7 sig. fig’s
12300
 3 sig. fig’s
 7 sig. fig’s

26. Practice: How many significant figures are there in 123000 1.23000
1.0
0.10

27. Operation with measurements
In general, no final result should be “more precise” than the original data from which it was derived.
Too vague.

28. Addition and subtraction with Sig. Figs
The sum or difference of two measurements is only as precise as the least precise one.
Example:
= 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 down) to how many digits after the decimal pt?
 1

29. Practice: 23.109 + 2.13 = ____ 12.7 + 3.31 = ____ 12.7 + 3.35 = ____
= ____
= = 25.24
= = 16.0
Must keep this 0.
3) = = 16.1
4) = 15.3 = 15.
Keep the decimal pt.

30. Multiplication and Division with Sig. Figs
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 =
=13.
Which number has the least number of sig. figs?
 5.5
How many sig figs?
 2
So the final answer should be rounded-off (up or down) to how many sig figs?
 2

31. Practice: 2.33/3.0 = ___ 2.33 / 3.0 = 0.7766667 = 0.78 2 sig figs

32. 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 = = 1.17
Note:
2.33 has the least number of sig. figs: 3

33. Prefixes Used with SI Units
Symbol
Fractions
nano n
× 10-9
micro 
× 10-6
milli m
× 10-3
centi c
× 10-2
kilo k
× 103
mega M
× 106
giga G
× 109
1 m = 1 × 10-6 m
1 mm = 1 × 10-3 m

34. Dimensional Analysis [x] = dimension of quantity x
What is the dimension of K if ?
Ignore

35. When angle in unit of radian

36. 1 ly = distance traveled by light in one year
HW 57
1 AU 1”
1 pc
1 ly = distance traveled by light in one year
Conversion factor to convert