Engineering
Fundamentals and Problem Solving, 6e
Chapter 7
Dimensions, Units and Conversions
Chapter Objectives
• Identify physical quantities in terms of
dimensions and units
• Differentiate between fundamental and derived
dimensions
• Understand the use of non-SI dimensional
systems (gravitational and absolute)
• Recognize base, supplementary, and derived SI
units
Engineering: Fundamentals and Problem Solving, 6e
Eide  Jenison  Northup  Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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Chapter Objectives – cont’d
• Apply the appropriate SI symbols and prefixes
• Describe the relationship between U.S.
Customary, Engineering System, and SI
• Systematically convert units from one system to
another
• Use knowledge of dimensions and units, along
with conversion rules, in the solution of
engineering problems.
Engineering: Fundamentals and Problem Solving, 6e
Eide  Jenison  Northup  Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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Progress towards Metrification
Engineers in the U.S. must be
prepared whatever system of
units they encounter.
With a large French Canadian
population, Canada has
adopted the metric system.
Canadian highway signs
Engineering: Fundamentals and Problem Solving, 6e
Eide  Jenison  Northup  Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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Dimensions
•
•
•
•
Independent of units
Fundamental or derived
Absolute system is based on mass (no gravity)
Gravitational system is based on force
Engineering: Fundamentals and Problem Solving, 6e
Eide  Jenison  Northup  Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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SI Units and Symbols
SI Units fall into 3 categories
1. Base Units
2. Supplementary Units
3. Derived Units
Engineering: Fundamentals and Problem Solving, 6e
Eide  Jenison  Northup  Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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SI Base Units
•
•
7 Base Units
Can be reproduced anywhere in the world
(except kg)
Engineering: Fundamentals and Problem Solving, 6e
Eide  Jenison  Northup  Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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SI Supplementary Units
•
•
•
May be considered base or derived units
Radian is commonly used. Steradian less so.
Radians are dimensionless
arc length = radius
radius
1 Radian: Angle when
arc length = radius
Engineering: Fundamentals and Problem Solving, 6e
Eide  Jenison  Northup  Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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SI derived units with names
Formed by combining
• Base
• Supplementary or
• Other derived units
Engineering: Fundamentals and Problem Solving, 6e
Eide  Jenison  Northup  Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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SI derived units without names
Some derived units have no special SI unit names or symbols
Engineering: Fundamentals and Problem Solving, 6e
Eide  Jenison  Northup  Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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Non-SI units accepted for use in U.S.
Certain units outside SI are accepted for use with SI in the
U.S. even though they diminish the system’s coherence.
Engineering: Fundamentals and Problem Solving, 6e
Eide  Jenison  Northup  Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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Unit Prefixes
Engineering: Fundamentals and Problem Solving, 6e
Eide  Jenison  Northup  Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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Significant Figures
SI prefix notations can be used to denote intended
significance
Distance
Precision
# of significant figures
10.000 km
9 999.5 to 10 000.5 m
5
10.00 km
9 995 to 10 005 m
4
10.0 km
9 950 to 10 050 m
3
10 km
5 000 to 15 000 m
1
Engineering: Fundamentals and Problem Solving, 6e
Eide  Jenison  Northup  Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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Significant Figures
Scientific notation can be used to denote intended
significance
Distance
Precision
# of significant figures
1.000 0 x 104 m
9 999.5 to 10 000.5 m
5
1.000 x 104 m
9 995 to 10 005 m
4
1.00 x 104 m
9 950 to 10 050 m
3
1.0 x 104 m
9 500 to 10 500 m
2
1 x 104 m
5 000 to 15 000 m
1
Engineering: Fundamentals and Problem Solving, 6e
Eide  Jenison  Northup  Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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Greek Alphabet
Engineering: Fundamentals and Problem Solving, 6e
Eide  Jenison  Northup  Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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