Chapter 7, Thinking Like an Engineer

1. Dimensions vs Units
   
   
   Dimensions: measurable physical idea
   
   
   Unit: quantifies a dimension
   
   
   Ex) 5 (value) meters (unit) is a measure of length (dimension)
   
   
   There are 7 main dimensions.
   
   
2. SI Prefixes
   
   
   "The SI system is based on multiples of 10."
   
   
   SI prefixes are used to simplify numbers with lots of zeroes. The prefixes coincide with values in engineering notation.
   
   
   Engineering notation: ###.### x 10^M
   M is a multiple of 3
   
   
   
   
   
3. The 7 fundamental dimensions & base units (these are important)
   
   
   
   
   
   
   
4. Official SI rules
   
   
   -Abbreviations with a capital letter are named after a specific person
   -Symbols also represent plural values

   Ex) cm = centimeter and centimeters

   -Symbols do not include periods
   -Symbols are recorded in upright Roman type to separate them from mathematical symbols, which are italicized
   -A single space separates units from symbols

   Exception: degree symbols for angles are written without a space between the value and the symbol

   Ex) 25 m

   -Values are grouped by threes as shown by spaces or commas
   -Symbols for derived units that contain several units are joined by a space or interpunct (center dot)
   

   Ex) kg m or kg•m

   -Symbols for derived units that are formed by dividing various units are joined by a virgule (a slash, /) or represented by a negative exponent
   

   Ex) m/s or m s^(-1)

   -It is incorrect to combine SI prefixes
   

   Ex) millimeters (mm)

   
   
   
   
5. Difference in SI, AES and USCS. What are they? Which do you prefer? Why?
   
   
   SI (Le Systeme International d'Unites) -metric system
   AES (American Engineering System) - used by the general public in the US
   USCS (United States customary System)- "English" units
   
   
   
   
   
   I prefer the SI system because I have had years of practice converting units based on multiples of 10 that it has become second nature.
   
   
6. Unit Conversion Procedure
   
   
   "We can multiply any expression by 1 without changing the expression."
   
   
   1. Write value and unit that you would like to convert.
   2. Write the conversion formula.
   3. Make a fraction (that equals 1) out of the conversion formula so that the units will cancel (original unit in numerator/denominator and the conversion unit in the opposite place)
   4. Multiply the original value and the resulting conversion formula together
   5. Cancel units, solve the equation, and express the answer in reasonable terms

   Ex) Convert 40 yds to ft.

   
   

          40 yds x (3 ft / 1 yd) = 120 ft 

   
   
   
   
7. Unit Conversion Procedure involving multiple steps
   
   
   1. Write value and unit that you would like to convert.
   2. Write the necessary conversion formulas
   3. Make fractions (that equal 1) out of the conversion formulas so that all the units will cancel (original unit in numerator/denominator and the conversion unit in the opposite place)
   4. Multiply the original value and the resulting conversion formulas together
   5. Cancel units, solve the equation, and express the answer in reasonable terms

   Ex)

   
   
   
   
   
   
   
8. Table 7-5 is very important to an Engineer
   
   
   
   
   
   
   
9. Comment on the note of caution under the 7-5 table and the paragraph above
   
   

   Derived units: There are currently 22 derived units all of which take the name of a famous scientist or engineer. There are common derived dimensions that currently do not have a corresponding, officially named derived SI unit.

   
   

   All measurable things can be represented by a combination of the seven original dimensions. The resulting units are referred to as derived units.
   
   
   Letters represent various quantities in a variety of disciplines. Be sure to examine and understand the nature of terms in each problem.
   
   
   ALWAYS INCLUDE UNITS IN CALCULATIONS
   
   
10. What is a Dimensionless Unit? Top of page 171 A dimensionless unit is a ratio or value that is unaccompanied by a corresponding unit. A radian is a dimensionless unit. A radian is the angle formed in the center of a circle by an arc whose length is equal to the circle's radius. Therefore, a radian is a ratio of a length (length of arc) divided by a length (length of radius), a value with units but without dimension.