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Understanding Units and Conversions: SI and US Customary Systems Explained

Dive into the world of units and conversions, exploring the significance of the SI (International System) and US Customary Systems. Learn about fundamental and derived dimensions, including base units like length, time, and mass. Understand engineering and scientific notation, coherent and noncoherent systems, and conversion factors essential in calculations. Whether it's discussing the ratio of an igloo's circumference to its diameter or the humorous 1 bannosecond, this guide provides clarity on how we measure and interpret quantities in different contexts.

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Understanding Units and Conversions: SI and US Customary Systems Explained

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Presentation Transcript

  1. Units and Conversions

  2. What is • Ratio of an igloo’s circumference to its diameter? • Eskimo π • Time between slipping on a peel and smacking the pavement? • 1 bannosecond • 1000 aches? • 1 killohurtz

  3. Quantity (Q) = Numerical Value * Units (U) Without the units to value has no meaning except as a ratio.

  4. Types of dimensions • Fundamental or base, what system is built on • Derived, the ones that are built on the base dimensions • For mechanical systems we have length, time, and mass or force as base

  5. SI System of Units (International System) • An absolute system (not gravity dependent) • Comes from the “metric system” or MKS • Base units: • Length: meter, m • Time: second, s • Mass: kilogram, kg Derived unit: Force, newton, N or kg m/s2

  6. SI System • Base units: • Length, meter • Time, second • Mass, kilogram • Electrical current, ampere • Temperature, kelvin • Amount of substance, mole • Luminous intensity, candela

  7. SI System • Supplemental Units: • Plane angle: radian, rad • Solid angle: steradian, sr • Derived Units: • See tables 6.4 and 6.5 on pg 207 • See figure 6.2 on pg 208 for relationships

  8. SI System • SI System is a base 10 system • Use prefix to identify size of unit • 109 giga G • 106 mega M • 103 kilo k • 10-3 milli m • 10-6 micro μ • 10-9 nano η

  9. Rules for Using SI Units • Look at section 6.6, pg 210 • Symbols and names • Multiplication and division • Numbers

  10. Engineering Notation • Scientific notation: number between 0 and 1.0 times 10 to a power, example 2.334 * 105m • Engineering notation: number between 0.1 and 1000 times 10 to a power of 3, 6, 9, -3, -6, -9, etc., example 233.4 km or 233.4 * 103 m

  11. Coherent and Noncoherent Systems Coherent systems: SI, US Customary No additional conversion factors needed Noncoherent systems: American Engineering System Additional conversion factor needed 1 lbf = 32.174 lbms2/ft

  12. US Customary System • Base units: • Length, foot, ft • Time, second, s • Force, pound, lb • Derived unit: • Mass, slug

  13. American Engineering System • Base units: • Length, ft • Time, s • Force, lbf • Derived unit: • Mass, lbm, 32.174 lbm = 1 slug

  14. Effect • For equation F = ma • SI system N = 1 kg m/s2 • USC system lb = 1 slug ft/s2 • Am Engr System lbf = 32.174 lbm ft/s2

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