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The main points are:Dimensions, Units, Conversions, Dimensional Homogeneity, Si Unit Prefixes, Customary Units, Mass and Weight, Magnitude of Dimension, Fundamental and Derived Dimensions, History of Units, Dimensional Analysis
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Assignment: Handout or visit website.
and derived. Fundamental are the most basic or elementary dimensions necessary to describe the physical state of an object. Derived dimensions are defined based upon scientific and engineering equations, and are a combination of fundamental dimensions.
Fundamental and Derived Dimensions
Velocity = Distance traveled / Elapsed time Distance traveled = Length (L) Elapsed time = Time (T) Velocity = Length / Time = L / T
dimensions for the three common systems of units.
Unit Systems and Conversions Exact Conversions
The internet provides valuable resources that can be used to obtain a variety of different conversion factors or completely carry out the conversions for you. Please refer to the following website:
Unit Systems and Conversions Example
miles per hour (mi/hr or mph) and wish to know your speed in feet per second (ft/s) and in meters per second (m/s) you would have to carry out the following conversions:
65
mi hr
5280
ft mi
⋅
1 60
hr min
⋅
1 60
min s
⋅ 95.
ft s
:= ⋅
ft s
1
m ft
⋅ 29.
m s
:= ⋅
( 125 day ⋅ ) 24 hr day
⋅
⋅ 60 min hr
⋅
⋅ 60 sec min
⋅
⋅ :=1.08 10 ⋅ 7 ⋅sec
16
lbm
ft 3
⋅
1
kg lbm
⋅
⋅ 3. ft m
⋅
3 ⋅ 256. kg
m^3
:= ⋅
a)
b)
Notice that the (ft/m) part is cubed because we cannot cancel out ft 3 with just ft, remember , the dimensions must be the same.