College PhysicsChapter 1

Introduction

Theories and ExperimentsThe goal of physics is to develop theories

based on experiments

A theory is a “guess,” expressed mathematically, about how a system works

The theory makes predictions about how a system should work

Experiments check the theories’ predictions

Every theory is a work in progress

Fundamental Quantities and Their Dimension

Length [L]

Mass [M]

Time [T]other physical quantities can be constructed from

these three

UnitsTo communicate the result of a measurement

for a quantity, a unit must be defined

Defining units allows everyone to relate to the same fundamental amount

Systems of MeasurementStandardized systems

agreed upon by some authority, usually a governmental body

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

Systems of Measurements, cont

cgs – Gaussian systemnamed for the first letters of the units it uses for

fundamental quantities

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

fundamental quantity

LengthUnits

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

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

MassUnits

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

Defined in terms of kilogram, based on a specific cylinder kept at the International Bureau of Weights and Measures

Standard Kilogram

TimeUnits

seconds, s in all three systems

Defined in terms of the oscillation of radiation from a cesium atom

US “Official” Atomic Clock

Approximate ValuesVarious tables in the text show approximate

values for length, mass, and timeNote the wide range of valuesLengths – Table 1.1Masses – Table 1.2Time intervals – Table 1.3

PrefixesPrefixes correspond to powers of 10

Each prefix has a specific name

Each prefix has a specific abbreviation

See table 1.4

Structure of MatterMatter is made up of molecules

the smallest division that is identifiable as a substance

Molecules are made up of atomscorrespond to elements

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

orbited byelectrons, negatively charges, “light”

fundamental particle, no structure

Structure of Matter

Dimensional AnalysisTechnique to check the correctness of an

equation

Dimensions (length, mass, time, combinations) can be treated as algebraic quantities add, subtract, multiply, divide

Both sides of equation must have the same dimensions

Dimensional Analysis, cont.

Cannot give numerical factors: this is its limitation

Dimensions of some common quantities are listed in Table 1.5

Uncertainty in Measurements

There is uncertainty in every measurement, this uncertainty carries over through the calculationsneed a technique to account for this

uncertainty

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

Significant FiguresA significant figure is one that is reliably

known

All non-zero digits are significant

Zeros are significant whenbetween other non-zero digitsafter the decimal point and another significant

figurecan be clarified by using scientific notation

Operations with Significant Figures

Accuracy – number of significant figures

When 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 of the factors being combined

Operations with Significant Figures, cont.

When adding or subtracting, round the result to the smallest number of decimal places of any term in the sum

If the last digit to be dropped is less than 5, drop the digit

If the last digit dropped is greater than or equal to 5, raise the last retained digit by 1

ConversionsWhen units are not consistent, you may

need to convert to appropriate ones

Units can be treated like algebraic quantities that can “cancel” each other

See the inside of the front cover for an extensive list of conversion factors

Example:

Examples of various units measuring a quantity

Order of MagnitudeApproximation based on a number of

assumptionsmay need to modify assumptions if more precise

results are needed

Order of magnitude is the power of 10 that applies

Coordinate SystemsUsed to describe the position of a point in space

Coordinate system consists ofa fixed reference point called the originspecific axes with scales and labels instructions on how to label a point relative to the

origin and the axes

Types of Coordinate Systems

Cartesian

Plane polar

Cartesian coordinate system

Also called rectangular coordinate system

x- and y- axes

Points are labeled (x,y)

Plane polar coordinate system

Origin and reference line are noted

Point is distance r from the origin in the direction of angle , ccw from reference line

Points are labeled (r,)

Trigonometry Review

More TrigonometryPythagorean Theorem

To find an angle, you need the inverse trig functionfor example,

Be sure your calculator is set appropriately for degrees or radians

Problem Solving Strategy

Problem Solving StrategyRead the problem

Identify the nature of the problem

Draw a diagramSome types of problems require very specific

types of diagrams

Problem Solving cont.Label the physical quantities

Can label on the diagramUse letters that remind you of the quantity

Many quantities have specific lettersChoose a coordinate system and label it

Identify principles and list dataIdentify the principle involvedList the data (given information)Indicate the unknown (what you are looking

for)

Problem Solving, cont.

Choose equation(s)Based on the principle, choose an equation or

set of equations to apply to the problem

Substitute into the equation(s)Solve for the unknown quantitySubstitute the data into the equationObtain a result Include units

Problem Solving, finalCheck the answer

Do the units match?Are the units correct for the quantity being found?

Does the answer seem reasonable? Check order of magnitude

Are signs appropriate and meaningful?

Problem Solving SummaryEquations are the tools of physics

Understand what the equations mean and how to use them

Carry through the algebra as far as possibleSubstitute numbers at the end

Be organized