dimensionalreasoning：空間推理(已修改)
2025-01-24 07:46 本頁(yè)面
【正文】 Dimensions Dimensional Reasoning Dimensions Dimensions and Measurements ? “Dimension” is characteristic of the object, condition, or event and is described quantitatively in terms of defined “units”. ? A physical quantity is equal to the product of two elements: – A quality or dimension – A quantity expressed in terms of “units” ? Dimensions – Physical things are measurable in terms of three primitive qualities (Maxwell 1871) ? Mass (M) ? Length (L) ? Time (T) Note: (Temperature, electrical charge, chemical quantity, and luminosity were added as “primitives” some years later.) Dimensions – Examples ? Length (L) ? Velocity (L/T) ? Force (ML/T2) ? Units – Measurements systemscgs, MKS, SIdefine units – SI units are now the international standard (although many engineers continue to use Imperial or .) Dimensions and Measurements (cont.) Dimensions SI Primitives DIMENSION UNIT SYMBOL for UNIT Length meter m Mass kilogram kg Time second s Elec. Current ampere A luminous intensity candela cd amount of substance mole mol Dimensions SI Derived units DESCRIPTION DERIVED UNIT SYMBOL DIMENSION Force newton N mkg/s2 Energy joule J m2kg/s2 Pressure pascal Pa kg/(ms2) Power watt W m2kg/s3 Dimensions Dimensional analysis ? Fundamental rules: – All terms in an equation must reduce to identical primitive dimensions – Dimensions can be algebraically manipulated, . – Example: ? Uses: – Check consistency of equations – Deduce expression for physical phenomenon TLTL ??221 ats ? LTTL ?? 22Dimensions Dimensional analysis distance s = s0 +vt2 + constant = p + ρgh +ρv2/2 volume of a torus = 2π2(Rr)2 222)s i n()s i n()s i n(cba??? ??Dimen
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