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UNITS (Syst é me Internationale)

UNITS (Syst é me Internationale). Standard Kilogram at S è vres. Conversion Factors. They are simply ratios that are equal to 1 e.g. These ratios make converting units easy! e.g. Conversion Factors. The most holy of conversion factors: 1 inch = 2.54 centimeters. Dimensional Analysis.

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UNITS (Syst é me Internationale)

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  1. UNITS (Systéme Internationale)

  2. Standard Kilogram at Sèvres

  3. Conversion Factors • They are simply ratios that are equal to 1 e.g. • These ratios make converting units easy! e.g.

  4. Conversion Factors • The most holy of conversion factors: 1 inch = 2.54 centimeters

  5. Dimensional Analysis Dimensions & units can be treated algebraically.

  6. Dimensional Analysis Checking equations with dimensional analysis: (L/T2)T2=L L (L/T)T=L • Each term must have same dimension • Two variables can not be added if dimensions are different • Multiplying variables is always fine • Numbers (e.g. 1/2 or p) are dimensionless

  7. Example 1.1 Check the equation for dimensional consistency: Here, m is a mass, g is an acceleration,c is a velocity, h is a length

  8. Example 1.2 Consider the equation: Where m and M are masses, r is a radius andv is a velocity. What are the dimensions of G ? L3/(MT2)

  9. Example 1.3 Given “x” has dimensions of distance, “u” has dimensions of velocity, “m” has dimensions of mass and “g” has dimensions of acceleration. Is this equation dimensionally valid? Yes Is this equation dimensionally valid? No

  10. Units vs. Dimensions • Dimensions: L, T, M, L/T … • Units: m, mm, cm, kg, g, mg, s, hr, years … • When equation is all algebra: check dimensions • When numbers are inserted: check units • Units obey same rules as dimensions:Never add terms with different units • Angles are dimensionless but have units (degrees or radians) • In physics sin(Y) or cos(Y) never occur unless Y is dimensionless

  11. Example 1.3 Grandma traveled 27 minutes at 44 m/s. How many miles did Grandma travel? 44.3 miles

  12. Prefixes In addition to mks units, standard prefixes can be used, e.g., cm, mm, mm, nm

  13. Example 1.4a The above expression yields: 40.11 m 4011 cm A or B Impossible to evaluate (dimensionally invalid)

  14. Example 1.4b The above expression yields: 4.5 m kg 4.5 g km A or B Impossible to evaluate (dimensionally invalid)

  15. Example 1.4b The above expression yields: -1.5 m -1.5 kg m2 -1.5 kg Impossible to evaluate (dimensionally invalid)

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