College PhysicsCollege Physics

Introduction Introduction

andand

Chapter 1Chapter 1

MeasurementsMeasurements

Basis of testing theories in scienceBasis of testing theories in science Need to have consistent systems Need to have consistent systems

of units for the measurementsof units for the measurements Uncertainties are inherentUncertainties are inherent Need rules for dealing with the Need rules for dealing with the

uncertaintiesuncertainties

Systems of MeasurementSystems of Measurement

Standardized systemsStandardized systems agreed upon by some authority, agreed upon by some authority,

usually a governmental bodyusually a governmental body SI -- SystSI -- Systééme Internationalme International

agreed to in 1960 by an international agreed to in 1960 by an international committeecommittee

main system used in this textmain system used in this text also called mks for the first letters in also called mks for the first letters in

the units of the fundamental quantitiesthe units of the fundamental quantities

Basic Quantities and Their Basic Quantities and Their DimensionDimension

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

Standard KilogramStandard Kilogram

Dimensional AnalysisDimensional Analysis

Technique to check the Technique to check the correctness of an equationcorrectness of an equation

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

Both sides of equation must have Both sides of equation must have the same dimensionsthe same dimensions

Operations with Significant Operations with Significant FiguresFigures

Accuracy -- number of significant Accuracy -- number of significant figuresfigures

When multiplying or dividing, round When multiplying or dividing, round the result to the same accuracy as the result to the same accuracy as the least accurate measurementthe least accurate measurement

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

ConversionsConversions

When units are not When units are not consistent, you may consistent, you may need to convert to need to convert to appropriate onesappropriate ones

Units can be treated like Units can be treated like algebraic quantities that algebraic quantities that can divide outcan divide out

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

How Fast is 1 m/s?

Examples of various units Examples of various units measuring a quantitymeasuring a quantity

Order of MagnitudeOrder of Magnitude

Approximation based on a number Approximation based on a number of assumptionsof assumptions may need to modify assumptions if may need to modify assumptions if

more precise results are neededmore precise results are needed Order of magnitude is the power of Order of magnitude is the power of

10 that applies10 that applies

Cartesian coordinate Cartesian coordinate systemsystem

also called also called rectangular rectangular coordinate coordinate systemsystem

x- and y- axesx- and y- axes points are labeled points are labeled

(x,y)(x,y)

Plane polar coordinate Plane polar coordinate systemsystem

origin and origin and reference line are reference line are notednoted

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

points are labeled points are labeled (r,(r,))

Trigonometry ReviewTrigonometry Review

sin

sideadjacent

sideopposite

hypotenuse

sideadjacent

hypotenuse

sideopposite

tan

cos

sin

More TrigonometryMore Trigonometry

Pythagorean TheoremPythagorean Theorem

To find an angle, you need the To find an angle, you need the inverse trig functioninverse trig function for example, for example,

Slide 15

Fig. 1.7, p.14