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SJSU PHYS 2A - Chapter 1

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College PhysicsChapter 1IntroductionTheories and Experiments The goal of physics is to develop theories based on experiments A physical 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 progressFundamental Quantities and Their Dimension Length [L] Mass [M] Time [T] Other physical quantities can be constructed from these threeUnits To communicate the result of a measurement for a quantity, a unit must be defined Defining units allows everyone to relate to the same fundamental amountSystems of Measurement Standardized systems Agreed upon by some authority, usually a governmental body SI – Systéme International Agreed to in 1960 by an international committee Main system used in this textLength Units SI – meter, m Defined in terms of a meter – the distance traveled by light in a vacuum during a given time Also establishes the value for the speed of light in a vacuumMass Units SI – kilogram, kg Defined in terms of kilogram, based on a specific cylinder kept at the International Bureau of Weights and MeasuresStandard KilogramTime Units seconds, s Defined in terms of the oscillation of radiation from a cesium atomApproximate Values Various tables in the text show approximate values for length, mass, and time Note the wide range of values Lengths – Table 1.1 Masses – Table 1.2 Time intervals – Table 1.3Other Systems of Measurements cgs – Gaussian system Named for the first letters of the units it uses for fundamental quantities US Customary Everyday units Often uses weight, in pounds, instead of mass as a fundamental quantityPrefixes Prefixes correspond to powers of 10 Each prefix has a specific name Each prefix has a specific abbreviation See table 1.4Structure of Matter Matter is made up of molecules The smallest division that is identifiable as a substance Molecules are made up of atoms Correspond to elementsMore structure of matter Atoms are made up of Nucleus, very dense, contains Protons, positively charged, “heavy” Neutrons, no charge, about same mass as protons Protons and neutrons are made up of quarks Orbited by Electrons, negatively charges, “light” Fundamental particle, no structureStructure of MatterDimensional Analysis Technique 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 dimensionsDimensional Analysis, cont. Cannot give numerical factors: this is its limitation Dimensions of some common quantities are listed in Table 1.5 Allows a check for calculations which can show up in the unitsUncertainty 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 calculationsSignificant Figures A significant figure is a reliably known digit All non-zero digits are significant Zeros are significant when Between other non-zero digits After the decimal point and another significant figure Can be clarified by using scientific notationOperations with Significant Figures Accuracy – number of significant figures Least accurate number has the lowest 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 combinedOperations 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 1Conversions When units are not consistent, you may need to convert to appropriate ones See the inside of the front cover for an extensive list of conversion factors Units can be treated like algebraic quantities that can “cancel” each other  Example:2.5415.0 38.11cmin cmin× =Estimates Can yield useful approximate answers An exact answer may be difficult or impossible Mathematical reasons Limited information available Can serve as a partial check for exact calculationsOrder of Magnitude Approximation based on a number of assumptions May need to modify assumptions if more precise results are needed Order of magnitude is the power of 10 that appliesCoordinate Systems Used to describe the position of a point in space Coordinate system consists of A fixed reference point called the origin, O Specified axes with scales and labels Instructions on how to label a point relative to the origin and the axesTypes of Coordinate Systems Cartesian  Plane polarCartesian 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 θ, ccw from reference line Points are labeled (r,θ)Trigonometry Reviewsin cos tan opposite sidehypotenuseadjacent sidehypotenuseopposite sideadjacent sideθθθ===More Trigonometry Pythagorean Theorem r2= x2+ y2 To find an angle, you need the inverse trig function For example, θ= sin-10.707 = 45°Degrees vs. Radians Be sure your calculator is set for the appropriate angular units for the problem For example: tan -10.5774 = 30.0° tan -10.5774 = 0.5236 radRectangular  Polar Rectangular to polar Given x and y, use Pythagorean theorem to find r Use x and y and the inverse tangent to find angle Polar to rectangular x = r cos θ y = r sin θProblem Solving StrategyProblem Solving Strategy Read the problem Identify the nature of the problem Draw a diagram Some types of problems require very specific types of diagramsProblem Solving cont. Label the physical quantities Can label on the diagram Use letters that remind you of the quantity Many quantities have


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