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2053 College Physics

Chapter 1Introduction

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Fundamental Quantities and Their Dimension

Length [L]Mass [M]Time [T]

other physical quantities can be constructed from these three

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Systems of Measurement

SI -- Systéme Internationalagreed to in 1960 by an international committeemain system used in this textalso called mks for the first letters in the units of the fundamental quantities (meter, kilogram, second)

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Systems of Measurements, cont

cgs – Gaussian systemnamed for the first letters of the units it uses for fundamental quantities (centimeter, gram, second)

US Customaryeveryday unitsoften uses weight, in pounds, instead of mass as a fundamental quantity

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Length

UnitsSI – meter, mcgs – centimeter, cmUS Customary – foot, ft

meter – the distance traveled by light in a vacuum during a given time

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MassUnits

SI – kilogram, kgcgs – gram, gUSC – slug, slug

kilogram, mass of a cylinder kept at the International Bureau of Weights and Measures, a “standard” of mass

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Standard Kilogram

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Time

Unitsseconds, s in all three systems

Certain number of oscillations of radiation from a cesium atom

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US “Official” Atomic Clock

10Table 1-1, p3.

11Table 1-2, p.3

12Table 1-3, p.3

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Prefixes

Prefixes correspond

to powers of 10Each prefix

has a specific abbreviation

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Structure of Matter

Matter is made up of moleculesthe smallest division that is identifiable as a (chemical) substance

Molecules are made up of atomscorrespond to elements (as in periodic table of elements)

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More structure of matterAtoms are made up of

nucleus, very dense, containsprotons, positively charged, “heavy”neutrons, no charge, about same mass as protons

protons and neutrons are made up of quarks

nucleus is orbited byelectrons, negatively charges, “light”

Quarks and electrons are viewed as fundamental particle, no structure (or we have not discovered it yet…keep looking)

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Structure of Matter

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Dimensional AnalysisTechnique to check the correctness of an equation, or correctness of a solutionDimensions (length, mass, time, combinations) can be treated as algebraic quantities

add, subtract, multiply, divideBoth sides of equation must have the same dimensions (cannot compare apples to oranges in an equation…)

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Dimensional Analysis, cont.

Cannot give numerical factors: this is its limitationDimensions of some common quantities are listed in Table 1.5

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Uncertainty in Measurements

There is uncertainty in every measurement, this uncertainty carries over through the calculations

need a technique to account for this uncertainty

We will use rules for significant figures to approximate the uncertainty in results of calculations

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Significant FiguresA significant figure is one that is reliably knownAccuracy – number of significant figuresWhen multiplying or dividing two or more quantities, the number of significant figures in the final result is the same as the number of significant figures in the least accurate

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Operations with Significant Figures

When adding or subtracting, round the result to the smallest number of decimal places of any term in the sumIf the last digit to be dropped is less than 5, drop the digitIf the last digit dropped is greater than or equal to 5, raise the last retained digit by 1

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ConversionsWhen units are not consistent, you may need to convert to appropriate onesUnits can be treated like algebraic quantities that can “cancel” each other See the table on the class web site for an extensive list of conversion factorsExample: want to convert inches to cm

2.5415.0 38.11

cmin cmin

× =

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Examples of various units measuring a quantity

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Order of Magnitude

Crude approximation Viewed as an “estimate”Order of magnitude is the power of 10 that applies

25Table 1-1, p3.

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Coordinate Systems

Used to describe the position of a point in spaceCoordinate system consists of

a fixed reference point called the originspecific axes with scales and labels

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Types of Coordinate Systems

Cartesian (also called rectangular)Plane polar

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Cartesian coordinate system

Also called rectangular coordinate systemx- and y- axes Points are labeled (x,y)

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Plane polar coordinate system

Origin and reference line are notedPoint is distance r from the origin in the direction of angle θ, counterclockwise from reference linePoints are labeled (r,θ)

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Trigonometry Review

sin

cos

tan

opposite sidehypotenuseadjacent sidehypotenuse

opposite sideadjacent side

θ

θ

θ

=

=

=

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More TrigonometryPythagorean Theorem

To find an angle, you need the inverse trig function

for example, if sinθ=0.707, then

Be sure your calculator is set appropriately for degrees or radians

2 2 2r x y= +

1sin 0.707 45θ −= = °

32Fig. P1-43, p.21

Check Pythagorean Theorem:5²=4²+3², or 25=16+9,Also 3=5×sinθ, or 4=5×cosθ

33Fig. 1-10, p.17

34Fig. P1-39, p.21

35Fig. 1-8, p.15

36Fig. P1-41, p.21