Units and Dimensions

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Units and Dimensions

• Class 6.2

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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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Units Dimensions

• A system of units is described by
• a set of fundamental dimensions from which all
  other dimensions may be derived, and
• a set of base units.

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Dimensions
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Base Units
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The International System of Units (SI)
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What are these things?

• See fundamentalSI.ppt for information about these
  'things'

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SI Prefixes
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Supplementary SI Dimensions
Supplementary Dimension
Base Unit
plane angle solid angle
radian (rad) steradian (sr)
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SI System of UnitsForce (mass) (acceleration)
Fma Wmg
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SI System of Units Force

• Force ma
• Newton
• N

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SI System of Units Work/Energy

• Work/ Energy Force X Distance
• N.m
• Joule
• J

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SI System of Units Power

• Power Work / Time
• Watt
• W

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SI System of Units Stress/Pressure

• Pressure Force / Area
• Pascal
• Pa

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U.S. Customary System of Units (USCS)
Derived Dimension
Unit
Definition
lbf sec2/ft
mass FT2/L
slug
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USCS Force (mass)(acceleration)
F ma W mg
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American Engineering System of Units (AES)
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American Engineering System

• Note, there is a problem when we use the same
  unit (pound, meaning lbf and lbm) to describe
  two different dimensions.
• Newton's Second Law F ma
• ? 1 lbf 1 lbm ft/s2 ??? NO!!!
• Must have consistency of units.

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Consistency of Units

• Principle of consistency of units
• units on the left side of an equation must be the
  same as those on the right side of an equation
• dimensional homogeneity

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AES and Newtons Law

• Must maintain dimensional homogeneity
• Now we have lbf lbf
• See gcderived.ppt for the derivation of gc

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Units

• What do students in ENGR 111 need to know about
  these system of Units?
• See Units.doc

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Typical Units Conversion

• Converting Between Foot and Meter
• To convert from foot to meter, multiply by
• 3.048 E-01
• To convert from foot to meter, multiply by
• (3.048 E-01)-1

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Thought Item

• Concerning the previous slide, which of the
  following is true?
• a. There are exactly 0.3048 m/ft.
• b. There are exactly 0.3048 ft/m.
• c. Neither a not b.
• Hint Think about this physically..

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Pairs Exercise (5 min.)

• Suppose you needed a metric drawing of the front
  view of a 6x6x6 box.
• At a scale of 110, would it fit on an A size
  sheet of paper (portrait or landscape) with ¼
  margins?
• Did you need to do unit conversion?
• How long would you draw each side on the metric
  drawing?

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Another Type of Units Conversion

• The force of wind acting on a body can be
  computed by the formula
• F 0.00256 Cd V2 A
• where F wind force in lbf , Cd drag
  coefficient (no units), V wind velocity in
  miles per hour and A projected area in ft2
• Is this dimensionally homogeneous?
• What are the units of 0.00256?
• More in Class 9.2

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Reality Check...

• Are units really important?
• Is checking your work and your teams work really
  important?

• Mars Lander (ABC news)
• Mars Lander (NASA)

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Assignment 10

• INDIVIDUAL ASSIGNMENT
• Due
• Foundations 13.1, 13.2