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inst07.1 - Class 7.1 Units Significant Digits and...

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Class 7.1 Units, Significant Digits, and Proportionality
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Objectives Know the difference between units and  dimensions Understand the SI, USCS, and AES  systems of units Know the SI prefixes from nano- to giga- Understand and apply the concept of  dimensional homogeneity
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Objectives What is the difference between an  absolute and a gravitational system of  units? What is a coherent system of units?  Apply dimensional homogeneity to  constants and equations.
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RAT 1
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Dimensions & Units Dimension - abstract quantity (e.g. length) Unit - a specific definition of a dimension based upon a physical reference (e.g. meter)
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What does a “unit” mean? Rod of unknown length Reference: Three rods of 1-m length The unknown rod is 3 m long. How long is the rod? unit number The number is meaningless without the unit!
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How do dimensions behave in mathematical formulae? Rule 1 - All terms that are added or subtracted must have same dimensions C B A D - + = All have identical dimensions
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How do dimensions behave in mathematical formulae? Rule 2 - Dimensions obey rules of multiplication and division L] [ ] [L [M] [L] ] [T ] [T [M] 2 2 2 = = = C AB D
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How do dimensions behave in mathematical formulae? Rule 3 - In scientific equations, the arguments of “transcendental functions” must be dimensionless. x D x B x C x A 3 ) exp( ) sin( ) ln( = = = = x must be dimensionless Exception - In engineering correlations, the argument may have dimensions Transcendental Function - Cannot be given by algebraic expressions consisting only of the argument and constants. Requires an infinite series ··· ! 3 ! 2 1 3 2 + + + + = x x x e x
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Dimensionally Homogeneous Equations An equation is said to be dimensionally homogeneous if the dimensions on both sides of the equal sign are the same.
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