Dimension “A physical property being measured". SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Definitions Qualitative – Asks what? Quantitative – How much? Unit “Addresses the quantitative aspect of a dimension".

SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Examples DimensionSymbolUnitExample LengthLmeters foot Length of room Stopping distance AreaL2L2 meters 2 foot 2 Area of room floor Cross-section of I-beam TimeTsecondsStopping time of car Flight time of arrow MassMkilograms slug Mass of engine block Mass of electron ForceFnewtons pounds Weight of rocket Rocket engine thrust

Dimensions are classified as one of three types: (1) fundamental (2) supplementary (3) derived SWTJC STEM – ENGR 1201 DimAnalysis cg13d Dimensional Analysis Dimension Types

Fundamental DimensionSymbol LengthL MassM TimeT ForceF Temperature  (theta) Electric currentA Electric chargeQ Molecular substancen Luminous intensityI SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Fundamental Dimensions Fundamental dimensions “Certain fundamental qualities such as length, mass, force, and time are symbolized with a single letter.”

Dimensional System “Minimum set of fundamental dimensions and associated base units that cover all needed physical properties for a field of science or engineering”. Seven such systems generally recognized internationally. See table 14.1 on page 365 of the text. Only two are used extensively, (1) SI (Systeme International) – Metric System (2) USCS (United States Customary System) SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Fundamental Dimensions Dimensional Systems

SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Fundamental Dimensions SI (Metric) SI - Systeme International or Metric System Fundamental DimensionSymbol 1. LengthL 2. MassM 3. TimeT 4. Temperature  (theta) 5. Electric currentA 6. Molecular substancen 7. Luminous intensityI Base Unit meter (m) kilogram (kg) second (s) kelvin (K) ampere (A) mole (mol) candela (cd) Note: Force and charge are not fundamental dimensions.

SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Fundamental Dimensions USCS USCS - United States Customary System Fundamental DimensionSymbol 1. LengthL 2. ForceF 3. TimeT 4. Temperaturet 5. Electric currentA 6. Molecular substancen 7. Luminous intensityI Base Unit foot (ft) pound (lb) second (s) rankine (R) ampere (A) mole (mol) candela (cd) Note: Mass and charge are not fundamental dimensions.

SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Fundamental Dimensions Absolute vs. Gravitational SI (Systeme International) 1 In SI, force is derived from mass (F ~ M. L/T 2 ) making the force unit a kg. m/s 2 that is called a newton (N). 2 The use of the letter "A" to refer to both the dimension and the unit is a bit confusing. You will have to rely on the context of its use to determine which it is. (1)In the USCS system, force is a fundamental dimension. A standard weight is involved in the definition of force tying the USCS system to gravitational effects. The USCS system is called a gravitational system. For earthbound problems this fine, but for space mechanics it presents difficulties. (2)In the SI system, mass is a fundamental dimension making the entire system independent of gravitational considerations. For this reason, the SI system is called an absolute system. It works everywhere!

Dimensions are classified as one of three types: (1) fundamental SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Types of Dimensions Supplementary (2) supplementary

SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Supplementary Dimensions SI (Systeme International) 1 In SI, force is derived from mass (F ~ M. L/T 2 ) making the force unit a kg. m/s 2 that is called a newton (N). 2 The use of the letter "A" to refer to both the dimension and the unit is a bit confusing. You will have to rely on the context of its use to determine which it is. Supplementary DimensionsSymbol Unit (abbrev.) Plane angleθ radian (rad) Solid angleβ steradian (sr) Supplementary dimensions “Embody geometric concepts needed in the mathematical formulation of natural laws".

Dimensions are classified as one of three types: (1) fundamental (2) supplementary SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Types of Dimensions Derived (3) derived

1.Fundamental dimension – Length L Base unit – m (meters) Derived dimension – Area L 2 Base unit – m 2 (meters squared) SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Types of Dimensions Derived Derived dimensions “Associated with physical properties that can be written as some combination of fundamental dimensions". L L L Length 2 m Area L. L = L 2 4 m 2 Base Unit Symbol Dimension

2.Fundamental dimension – Force F Base unit – lb (pound) Derived dimension – Pressure (force per unit of area) = F/L 2 Base unit – lb/ft 2 (pounds per foot squared) SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Types of Dimensions Derived Derived dimensions “Associated with physical properties that can be written as some combination of fundamental dimensions". Force F lb (pounds) L (ft) F (lb) (Distributed) Pressure Force /Area F/L 2 lb/ft 2

SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Derived Dimensions SI

SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Derived Dimensions USCS SI (Systeme International) 1 In SI, force is derived from mass (F ~ M. L/T 2 ) making the force unit a kg. m/s 2 that is called a newton (N). 2 The use of the letter "A" to refer to both the dimension and the unit is a bit confusing. You will have to rely on the context of its use to determine which it is.

SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Derived Dimensions Notes - Reduction SI (Systeme International) 1 In SI, force is derived from mass (F ~ M. L/T 2 ) making the force unit a kg. m/s 2 that is called a newton (N). 2 The use of the letter "A" to refer to both the dimension and the unit is a bit confusing. You will have to rely on the context of its use to determine which it is. (1)In every case, derived dimensions are completely expressible in terms of fundamental/supplementary dimensions as illustrated in the last column. This reflects the reduction process that holds for all dimensional systems. Can m/s be reduced?No. Has no derived units. Can N/m 2 be reduced?Yes. N (newton) is a derived unit.

SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Derived Dimensions Notes - Coherency SI (Systeme International) 1 In SI, force is derived from mass (F ~ M. L/T 2 ) making the force unit a kg. m/s 2 that is called a newton (N). 2 The use of the letter "A" to refer to both the dimension and the unit is a bit confusing. You will have to rely on the context of its use to determine which it is. (2)Another dimensional system characteristic is whether or not it is coherent. A coherent system "adheres to the principle that each derived unit is a product or quotient of base and supplementary units without any conversion factors". SI and USCS are coherent. AES (American Engineering System) is not. From Newton’s Second Law, SI and USCS Weight = m. g AESWeight = m. g / 32.17

SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Derived Dimensions Examples SI (Systeme International) 1 In SI, force is derived from mass (F ~ M. L/T 2 ) making the force unit a kg. m/s 2 that is called a newton (N). 2 The use of the letter "A" to refer to both the dimension and the unit is a bit confusing. You will have to rely on the context of its use to determine which it is.

SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Derived Dimensions Examples SI (Systeme International) 1 In SI, force is derived from mass (F ~ M. L/T 2 ) making the force unit a kg. m/s 2 that is called a newton (N). 2 The use of the letter "A" to refer to both the dimension and the unit is a bit confusing. You will have to rely on the context of its use to determine which it is. Note: a pascal (Pa) is a newton per square meter (N/m 2 )!

SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Derived Dimensions Examples SI (Systeme International) 1 In SI, force is derived from mass (F ~ M. L/T 2 ) making the force unit a kg. m/s 2 that is called a newton (N). 2 The use of the letter "A" to refer to both the dimension and the unit is a bit confusing. You will have to rely on the context of its use to determine which it is.

SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Derived Dimensions Examples SI (Systeme International) 1 In SI, force is derived from mass (F ~ M. L/T 2 ) making the force unit a kg. m/s 2 that is called a newton (N). 2 The use of the letter "A" to refer to both the dimension and the unit is a bit confusing. You will have to rely on the context of its use to determine which it is. h d

SWTJC STEM – ENGR 1201 DimAnalysis cg13a Dimensional Analysis Derived Dimensions Examples SI (Systeme International) 1 In SI, force is derived from mass (F ~ M. L/T 2 ) making the force unit a kg. m/s 2 that is called a newton (N). 2 The use of the letter "A" to refer to both the dimension and the unit is a bit confusing. You will have to rely on the context of its use to determine which it is. h d