ch1 - Chapter 1 Introduction and Vectors These brief notes...

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Chapter 1 Introduction and Vectors These brief notes are provided here to give the students a summary of the lectures given in class. The textbook should still be the complete source for the course.

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Theory and Experiments Should complement each other When a discrepancy occurs, theory may be modified Theory may apply to limited conditions Example: Newtonian Mechanics is confined to objects traveling slowly with respect to the speed of light Used to try to develop a more general theory
Standards of Quantities SI – Systéme International Most often used in the text Almost universally used in science and industry Length is measured in meters (m) Time is measured in seconds (s) Mass is measured in kilograms (kg)

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Prefixes The prefixes can be used with any base units They are multipliers of the base unit Examples: 1 mm = 10 -3 m 1 mg = 10 -3 g
Fundamental and Derived Quantities In mechanics, three fundamental quantities are used Length Mass Time Will also use derived quantities These are other quantities that can be expressed as a mathematical combination of fundamental quantities

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Density Density is an example of a derived quantity It is defined as mass per unit volume Units are kg/m 3 V m
Basic Quantities and Their Dimension Dimension has a specific meaning – it denotes the physical nature of a quantity Dimensions are denoted with square brackets Length – L Mass – M Time – T

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Dimensional Analysis Cannot give numerical factors: this is its limitation Dimensions of some common quantities are given below
Dimensional Analysis, example Given the equation: x = 1/2 a t 2 Check dimensions on each side: The T 2 ’s cancel, leaving L for the dimensions of each side The equation is dimensionally correct There are no dimensions for the constant L T T L L 2 2

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Conversion Always include units for every quantity, you can carry the units through the entire calculation Multiply original value by a ratio equal to one The ratio is called a conversion factor Example cm 1 . 38 in 1 cm 54 . 2 in 0 . 15 cm ? in 0 . 15
Order 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 applies In order of magnitude calculations, the results are reliable to within about a factor of 10

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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
Significant Figures A significant figure is one that is reliably

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This note was uploaded on 04/02/2010 for the course PHYSICS 6A taught by Professor Koskeshian during the Spring '10 term at UCLA.

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ch1 - Chapter 1 Introduction and Vectors These brief notes...

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