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

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

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)

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)

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

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

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

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)

PHY 205 Ch1: Measurements and Vectors

S6/7. Vectors

Definition of displacement: (1, 2 and 3 dim)

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):

PHY 205 Ch1: Measurements and Vectors

S6/7. Vectors

Properties of displacement:

Addition

• Components

• arrows

O x

y

PHY 205 Ch1: Measurements and Vectors

S6/7. Vectors Properties of displacement:

Multiplication by number

• Components

• arrows

O x

y

PHY 205 Ch1: Measurements and Vectors

S6/7. Vectors

Properties of displacement: cont’d

Subtraction

Basis vectors

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: