phy 205 ch1: measurements and vectors 1.nature of physics 2.units (and standards) 3.conversion of...
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PHY 205 Ch1: Measurements and Vectors
1. Nature of Physics2. Units (and standards)3. Conversion of units4. Dimensions of Physical Quantities5. Significant Figures and Order of Magnitude6. Vectors7. General Properties of Vectors
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PHY 205 Ch1: Measurements and Vectors
S1. Nature of Physics (no exercise – replaces section 1 of book)
A. Scientific Paradigm
Abstract Realm:Theories, models,…
Reality: all phenomena in the Universe
Theoretical Prediction
ExperimentalTest
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PHY 205 Ch1: Measurements and Vectors
1. Cont’d. Nature of Physics (no exercise – replaces section 1 of book)
B. Physics: the science of fundamental processes
Fundamental Science. Quantitative understanding of all processes involved
Complex systems: Large number of processes involved.
Fundamental Systems: Only a few processes at play
Empirical Science (Based on observation, no quantitative “understanding” of the processes involved)
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PHY 205 Ch1: Measurements and Vectors
S2. Units and standards (added topic: standards)
Measurements require material representation of concepts like distance, time etc. (ie physical quantities
These material representations are called standardsExample: bar with 2 scratches (obsolete now) for distance – called meter standard.
Unit correspond to the number assigned to the standarde.g. 100 to meter standard gives cm1 to standard gives the “ meter” unit.
Systeme International of units: SI system
Int. System (SI): m, s and kg. Fundamental (eg m ) or derived (eg N=kg m /s^2)
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PHY 205 Ch1: Measurements and Vectors
S3 Conversion of units
WSo for example, to convert : 12 ft2
12 ft2 = 12 ft2 x 12 = 12 ft2 x = 12 ft2 x = 1.12 m2
Alternative scheme (not in book): just replace one unit by its value in terms of the new unit:
10 ft3 = 10 (0.305 m)3 = 0.0284 m3
Unit prefixes: memorize the red ones in table 1-1 in book: centi, mille, micro, nano (pico), kilo, mega and giga
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PHY 205 Ch1: Measurements and Vectors
S4. Dimensions of Physical Quantities
Dimensions L: length; T: mass: M
Dimensions help check the validity of a result
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PHY 205 Ch1: Measurements and Vectors
S5. Significant figures and order of magnitude
Number: Sig figs
1024 4
1024.03 6
0.001241 4
0.0012410 5
102400 Ambiguous so use sci. notation
1.024x105 4
1.02400x105 6
Learn rules Rules:X or / : quote result with nb of sig figs = smallest nb of sig figs but careful about exact numbers like 2 in 2p r: sig figs used in r or p are the only relevant onesAnd for + or - : answer has sig figs corresponding to number with fewest decimal placesExamples:2 p r =2 x 3.14 x 2.1 =13.188 =1315.332-0.16= 15.172 = 15.1715.3-0.16=15.14 =15.1
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PHY 205 Ch1: Measurements and Vectors
S6/7. Vectors (slightly enhanced from book)
Rectangular Coordinate systems: (1, 2 and 3 dimensions)
The fact that we can erect a rectangular coordinate system in our universe is a hypothesis we make that has to be verified (and it is valid….most of the time)
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PHY 205 Ch1: Measurements and Vectors
S6/7. Vectors
Definition of displacement: (1, 2 and 3 dim)
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PHY 205 Ch1: Measurements and Vectors
S6/7. Vectors
Two representations of displacement (in 2 dimensions from now on):
Component form:
Graphical form (arrow with magnitude and direction):
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PHY 205 Ch1: Measurements and Vectors
S6/7. Vectors
Properties of displacement:
Addition
• Components
• arrows
O x
y
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PHY 205 Ch1: Measurements and Vectors
S6/7. Vectors Properties of displacement:
Multiplication by number
• Components
• arrows
O x
y
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PHY 205 Ch1: Measurements and Vectors
S6/7. Vectors
Properties of displacement: cont’d
Subtraction
Basis vectors
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PHY 205 Ch1: Measurements and Vectors
S6/7. Vectors
Definition of vector: quantities that have all same properties as displacement
Example velocity is displacement over time: