Phys 1111K Spring 2005 Introduction Main Sections Ch 1 Pre Requisites St in addition to ards in addition to Units

Phys 1111K Spring 2005 Introduction Main Sections Ch 1 Pre Requisites St in addition to ards in addition to Units www.phwiki.com

Phys 1111K Spring 2005 Introduction Main Sections Ch 1 Pre Requisites St in addition to ards in addition to Units

True, Margot, Food Editor has reference to this Academic Journal, PHwiki organized this Journal Phys 1111K Spring 2005 Course Overview Dr. Perera Room: 507 Science Annex Phone: 651-2709, 3221/3222 Introduction What is Physics Underst in addition to ing nature Laws of Physics Wide spread impact on modern technology Every minute of your life is involved in Physics Needs in addition to Uses Even without knowing it A Fundamental Science Welcome to Introduction to Physics Main Sections Kinematics Classical Mechanics (Chs 1-10) both Transnational in addition to Rotational Dynamics Fluid Mechanics (Ch 11) Thermodynamics (Chs 12-13) Heat Temperature

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Ch 1 Pre Requisites Co-ordinate System (Cartesian) Trigonometry Pythagorean Theorem Sin Cos Pythagorean Theorem Tan Algebra Quadratic Equations Powers of 10 Symbols x, , n, p St in addition to ards in addition to Units Why do we need st in addition to ard units King Louis Yard Royal foot SI Units Le System International Units meter : Light travels in a vacuum in time of 1/ 299792458 seconds kilogram : St in addition to ard cylinder of Pl-Iridium alloy at room temperature second : Cs-133 atomic clock – time as long as 9192631770 wave cycles to occur

Conversion of Units 1 meter = 100 centimeter = 1000 millimeter (mm) 103 meter = 1000 meters = 1 kilometer 0.001 meter = 10-3 meter = 1 millimeter 3.281 feet = 1 meter 5280 feet = 1 mile 3600 seconds = 1 hour 0.65 miles / hour = 95 feet / second = 29 meters / second Significant Figures Keep the same number of significant figures in the answer as in the least accurate number 3.5 × 10.6 = 37 (not 37.1) 0 ± 0.1 0 ± 0.1 35 39 Uncertainty : Quality of the apparatus Skill of the experimenter Number of measurements Dimensional Analysis Distance – [L] Mass – [M] Time – [T] Check whether an equation is mathematically correct Find an unknown exponent

Vectors in addition to Scalars Addition in addition to subtraction Multiplying by a number Components Vector addition by Components Vector addition by Graphing Vector Addition (Due East) Resultant Displacement R = A+ B Due East in addition to then Due north R = A +B 5 = 4 +3 Find Theta What if Vectors are not Perpendicular Can we say R = A +B But Pythagorean Theorem valid Graphical Technique A = 275 m, B =125 m Scale 1 cm = 10 m R = 228 m

Vector Components r = X + Y r A, X Ax Y AY Different Axes Vector Components depend on the orientation of the axes Scalar components (With positive or negative sign) Adding Vectors Using Components C = A +B, C = Cx + CY A = Ax +Ay CX = B = Bx + By CY =

Example 8 A+B=R A=Ax+Ay B=Bx+By Note By is in negative direction. Example 8 (continued) Example 8 (continued)

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Preparatory Physics (PYPY001 ) Coordinator:

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Preparatory Physics (PYPY001 ) Coordinator:

Dreyer, Steve, Executive Editor has reference to this Academic Journal, PHwiki organized this Journal Preparatory Physics (PYPY001)Coordinator: Prof.Dr.Hassan A.MohammedPreparatory Physics PYPY001

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Physical science is concerned with making sense out of the physical environment.Objects in the environment could be quite large, such as the Sun, the Moon, or even the solar system, or invisible to the unaided human eye. Objects can be any size, but people are usually concerned with objects that are larger than a pinhead in addition to smaller than a house. Outside these limits, the actual size of an object is difficult as long as most people to comprehend. CHAPTER 1 What Is Science A generalized mental image of objects called a concept. Your generalized mental image as long as the concept that goes with the word chair probably includes a four-legged object with a backrest. Not all of your concepts are about material objects. You also have concepts about intangibles such as time, motion, in addition to relationships between events. For example, the words second, hour, day, in addition to month represent concepts of time. Properties are the qualities or attributes that, taken together, are usually peculiar to an object. The properties of an object are the effect the object has on your senses. The description of any property implies some kind of referent. The word referent means that you refer to, or think of, a given property in terms of another,more familiar object.

1.2 QUANTIFYING PROPERTIES Assumptions in addition to vagueness can be avoided by using measurement in a description. Measurement is a process of comparing a property to a well-defined in addition to agreed-upon referent. The well-defined in addition to agreed-upon referent is used as a st in addition to ard called a unit. A measurement statement always contains a number in addition to name as long as the referent unit. The number answers the question “How much” in addition to the name answers the question “Of what” Thus, a measurement always tells you “how much of what.”1.3 MEASUREMENT SYSTEMSMeasurement is a process that brings precision to a description by specifying the “how much” in addition to “of what” of a property in a particular situation.When st in addition to ards are established, the referent unit is called a st in addition to ard unitThere are two major systems of st in addition to ard units in use today, the English system in addition to the metric system. Some adopted units of the English system were originally based on parts of the human body, presumably because you always had these referents with you (Figure 1.5). 1.4 STANDARD UNITS FORTHE METRIC SYSTEMThere are four properties that cannot be described in simpler terms, in addition to all other properties are combinations of these four. For this reason, they are called the fundamental properties.These four fundamental properties are (1) length,(2) mass, (3) time, in addition to (4) charge1.5 METRIC PREFIXESThe metric system uses prefixes to represent larger or smaller amounts by factors of 10. Some of the more commonly used prefixes, their abbreviations, in addition to their meanings are listed in Table 1.2.

1.6 UNDERSTANDINGS FROMMEASUREMENTSDATAMeasurement in as long as mation used to describe something is called data. Data can be used to describe objects, conditions, events, or changes that might be occurring.RATIOS AND GENERALIZATIONSOne mathematical technique as long as reducing data to a more manageable as long as m is to expose patterns through a ratio. A ratio is a relationship between two numbers that is obtained when one number is divided by another number.THE DENSITY RATIOSYMBOLS AND EQUATIONSSymbols:Symbols usually provide a clue about which quantity they represent, such as m as long as mass in addition to V as long as volume. The symbol m thus represents a quantity of mass that is specified by a number in addition to a unit, as long as example, 16 g. The symbol V represents a quantity of volume that is specified by a number in addition to a unit, such as 17 cm3.There are more quantities than upper- in addition to lowercase letters, however, so letters from the Greek alphabet are also used, as long as example, as long as mass density. Sometimes a subscript is used to identify a quantity in a particular situation, such as vi as long as initial, or beginning, velocity in addition to vf as long as final velocity. Some symbols are also used to carry messages; as long as example, the Greek letter delta () is a message that means “the change in” a value. Other message symbols are the symbol , which means “there as long as e,” in addition to thesymbol , which means “is proportional to.”EquationsAn equation, a statement that describes a relationship where the quantities on one side of the equal sign are identical to the quantities on the other side. The word identical refers to both the numbers in addition to the units. Thus, in the equation describing the property of density, = m/V, the numbers on both sides of the equal sign are identical (e.g., 5 = 10/2). The units on bothsides of the equal sign are also identical (e.g., g/cm3 = g/cm3).Equations are used to (1) describe a property, (2) define a concept, or (3) describe how quantities change relative to each other. The term variable refers to a specific quantity of an object or event that can have different values. Your weight, as long as example, is a variable because it can have a different value on different days.A change in the amount of food you eat results in a change in your weight A graph is used to help you picture relationships between variables.When two variables increase (or decrease) together in the same ratio, they are said to be in direct proportion. amount of food consumed weight gainSometimes one variable increases while a second variable decreases in the same ratio. This is an inverse proportion relationship.

Here are the as long as ms of these four different types of proportional relationships:Direct a bInverse a 1lbSquare a b2Inverse square a 1lb2Other common relationships include one variable increasing in proportion to the square or to the inverse square of a second variable.Proportionality StatementsTo make a statement of proportionality into an equation, you need to apply a proportionality constant, which is sometimes given the symbol k.For the fuel pump example, the equation is volume = (time)(constant) V = tkA proportionality constant in an equation might be a numerical constant,a constant that is without units. Such numerical constants are said to be dimensionle. The value of is usually rounded to 3.14.HOW TO SOLVE PROBLEMSStep 1: Read through the problem in addition to make a list of the variables with their symbols on the left side of the page, including the unknown with a question mark.Step 2: Inspect the list of variables in addition to the unknown, in addition to identify the equation that expresses a relationship between these variables.Step 3: If necessary, solve the equation as long as the variable in question.Step 4: If necessary, convert unlike units so they are all the same. For example, if a time is given in seconds in addition to a speed is given in kilo meters per hour, you should convert the km/h to m/s.Step 5: Now you are ready to substitute the number value in addition to unit as long as each symbol in the equation.Step 6: Do the indicated mathematical operations on the numbers in addition to on the units.Step 7: Now ask yourself if the number seems reasonable as long as the question that was asked, in addition to ask yourself if the unit is correct.Step 8: Draw a box around your answer (numbers in addition to units)

THE SCIENTIFIC METHODThere are different approaches in addition to different ways to evaluate what is found. Overall, the similar things might look like this:1. Observe some aspect of nature.2. Propose an explanation as long as something observed.3. Use the explanation to make predictions.4. Test predictions by doing an experiment or by making more observations.5. Modify explanation as needed.6. Return to step 3.There are at least three separate activities that seem to be common to scientists in different fields as they conduct scientific investigations, in addition to these generalizations look like this: Collecting observations Developing explanations Testing explanationsEXPLANATIONS AND INVESTIGATIONSA hypothesis is a tentative thought- or experiment-derived explanation. It must be compatible with observations in addition to provide underst in addition to ing of some aspect of nature, but the key word here is tentative. A hypothesis is tested by experiment in addition to is rejected, or modified, if a single observation or test does not fit.Testing a HypothesisThe successful testing of a hypothesis may lead to the design of experiments, or it could lead to the development of another hypothesis, which could, in turn, lead to the design of yet more experiments.Another common method as long as testing a hypothesis involves devising an experiment. An experiment is a re-creation of an event or occurrence in a way that enables a scientist to support or disprove a hypothesis.LAWS AND PRINCIPLESA scientific law describes an important relationship that is observed in nature to occur consistently time after time. Basically, scientific laws describe what happens in nature. The law is often identified with the name of a person associated with the as long as mulation of the law.Scientific principles in addition to laws do not dictate the behavior of objects; they simply describe it. They do not say how things ought to act but rather how things do act.A scientific principle describes a more specific set of relationships than is usually identified in a law. The difference between a scientific principle in addition to a scientific law is usually one of the extent of the phenomena covered by the explanation, but there is not always a clear distinction between the two.

MODELS AND THEORIESOften the part of nature being considered is too small or too large to be visible to the human eye, in addition to the use of a model is needed. A model is a description of a theory or idea that accounts as long as all known properties.At the other end of the size scale, models of atoms in addition to molecules are often used to help us underst in addition to what is happening in this otherwise invisible world.A theory is defined as a broad working hypothesisthat is based on extensive experimental evidence. A scientific theory tells you why something happens.

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EXAMPLE:A bicycle has an average speed of 8.00 km/h. How far will it travel in10.0 seconds (Answer: 22.2 m)VELOCITYThe word velocity is sometimes used interchangeably with the word speed, but there is a difference. Velocity describes the speed in addition to direction of a moving object. For example, a speed might be described as 60 km/h. A velocity might be described as 60 km/h to the west. To produce a change in velocity, either the speed or the direction is changed (or both are changed).Acceleration is defined as a change of velocity per unit time, orAcceleration

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Historical Introduction Agenda Fast Fourier Transform

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Historical Introduction Agenda Fast Fourier Transform

Strayer University-North Raleigh Campus, NC has reference to this Academic Journal, Fast Fourier TransformAgendaHistorical IntroductionCFT in addition to DFTDerivation of FFTImplementationHistorical Introduction

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Continuous Fourier Transform (CFT)Given: Complex Fourier Coefficient:Fourier Series: (change of basis)Given:Discrete Fourier TransformDiscrete Fourier TransformFourier-MatrixDFT of x:Matrix-Vector-Product:N^2 MultiplicationsN(N-1) AdditionsArithmetic Complexity: O(N^2)

Trigonometric InterpolationGiven: equidistant samples of i.e.Goal: find such that alongside Trigonometric InterpolationTheorem:=> Inverse DFT! Derivation of FFT

Historical Introduction Agenda Fast Fourier Transform

FFT ? Lower Bound:(S. Winograd ? Arithmetic Complexity of Computations 1980 CBMS-NSF, Regional Conference Series in Applied Mathematics)FFT if N is primeTwo approaches:Implementation (N = power of 2)

Recursive ImplementationRecursive ImplementationStack-Problem:Space Complexity: O(NlogN)Better Approach:Iterative Implementation => in place! (O(N))Iterative Implementation (N=8)

Iterative Implementation (N=8)Iterative Implementation (N=8)Bit-Inversion:Iterative ImplementationTheorem:The bit inversion yields the result of the permutation graph.

Iterative Implementation

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