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- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Introductory_Physics_II_(1112)/01%3A_Introduction_to_Physics_and_Measurements/1.06%3A_Dimensional_AnalysisFor example, if r is the radius of a cylinder and h is its height, then we write [r] = L and [h] = L to indicate the dimensions of the radius and height are both those of length, or L. Similarly, if w...For example, if r is the radius of a cylinder and h is its height, then we write [r] = L and [h] = L to indicate the dimensions of the radius and height are both those of length, or L. Similarly, if we use the symbol A for the surface area of a cylinder and V for its volume, then [A] = L 2 and [V] = L 3 . If we use the symbol m for the mass of the cylinder and ρ for the density of the material from which the cylinder is made, then [m] = M and [ρ] = ML −3 .
- https://phys.libretexts.org/Courses/Fresno_City_College/NATSCI-1A%3A_Natural_Science_for_Educators_Fresno_City_College_(CID%3A_PHYS_140)/02%3A_Units_Measurement_Graphing_and_Calculation/2.06%3A_Measurement/2.6.09%3A_Dimensional_AnalysisDimensional analysis is used in numerical calculations, and in converting units. It can help us identify whether an equation is set up correctly (i.e. the resulting units should be as expected). Units...Dimensional analysis is used in numerical calculations, and in converting units. It can help us identify whether an equation is set up correctly (i.e. the resulting units should be as expected). Units are treated similarly to the associated numerical values, i.e., if a variable in an equation is supposed to be squared, then the associated dimensions are squared, etc.
- https://phys.libretexts.org/Bookshelves/University_Physics/Mechanics_and_Relativity_(Idema)/01%3A_Introduction_to_Classical_Mechanics/1.02%3A_Dimensional_AnalysisAlthough you will of course need a complete physical model (represented as a set of mathematical equations) to fully describe a physical system, you can get surprisingly far with a simple method that ...Although you will of course need a complete physical model (represented as a set of mathematical equations) to fully describe a physical system, you can get surprisingly far with a simple method that requires no detailed knowledge at all. This method is known as dimensional analysis, and based on the observation in the previous section that the two sides of any physical equation have to have the same dimension. You can use this principle to qualitatively understand a system.
- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_II_(2212)/01%3A_Introduction_to_Physics_Measurements_and_Mathematics_Tools/1.06%3A_Dimensional_AnalysisThe derivative of a function is just the slope of the line tangent to its graph and slopes are ratios, so for physical quantities v and t, we have that the dimension of the derivative of v with respec...The derivative of a function is just the slope of the line tangent to its graph and slopes are ratios, so for physical quantities v and t, we have that the dimension of the derivative of v with respect to t is just the ratio of the dimension of v over that of t:
- https://phys.libretexts.org/Courses/Joliet_Junior_College/Physics_201_-_Fall_2019/Book%3A_Physics_(Boundless)/01%3A_The_Basics_of_Physics/1.5%3A_Units_and_Measurement_Redux/Dimensional_AnalysisThe dimension of a physical quantity is just an expression of the base quantities from which it is derived. All equations expressing physical laws or principles must be dimensionally consistent. This ...The dimension of a physical quantity is just an expression of the base quantities from which it is derived. All equations expressing physical laws or principles must be dimensionally consistent. This fact can be used as an aid in remembering physical laws, as a way to check whether claimed relationships between physical quantities are possible, and even to derive new physical laws.
- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_I_(2211)/01%3A_Introduction_to_Physics_Measurements_and_Mathematics_Tools/1.06%3A_Dimensional_AnalysisThe derivative of a function is just the slope of the line tangent to its graph and slopes are ratios, so for physical quantities v and t, we have that the dimension of the derivative of v with respec...The derivative of a function is just the slope of the line tangent to its graph and slopes are ratios, so for physical quantities v and t, we have that the dimension of the derivative of v with respect to t is just the ratio of the dimension of v over that of t:
- https://phys.libretexts.org/Courses/Tuskegee_University/Algebra_Based_Physics_I/01%3A_Nature_of_Physics/1.05%3A_Dimensional_AnalysisThe dimension of a physical quantity is just an expression of the base quantities from which it is derived. All equations expressing physical laws or principles must be dimensionally consistent. This ...The dimension of a physical quantity is just an expression of the base quantities from which it is derived. All equations expressing physical laws or principles must be dimensionally consistent. This fact can be used as an aid in remembering physical laws, as a way to check whether claimed relationships between physical quantities are possible, and even to derive new physical laws.
- https://phys.libretexts.org/Courses/Muhlenberg_College/MC%3A_Physics_121_-_General_Physics_I/01%3A_Units_and_Measurement/1.05%3A_Dimensional_AnalysisThe dimension of a physical quantity is just an expression of the base quantities from which it is derived. All equations expressing physical laws or principles must be dimensionally consistent. This ...The dimension of a physical quantity is just an expression of the base quantities from which it is derived. All equations expressing physical laws or principles must be dimensionally consistent. This fact can be used as an aid in remembering physical laws, as a way to check whether claimed relationships between physical quantities are possible, and even to derive new physical laws.
- https://phys.libretexts.org/Courses/Prince_Georges_Community_College/General_Physics_I%3A_Classical_Mechanics/05%3A_Units/5.04%3A_Units_as_an_Error-Checking_TechniqueIf the units are correct, it doesn’t necessarily mean your derivation is correct (since you could be off by a factor of 2, for example), but it does give you some confidence that you at least haven’t ...If the units are correct, it doesn’t necessarily mean your derivation is correct (since you could be off by a factor of 2, for example), but it does give you some confidence that you at least haven’t made a units error. Sometimes it’s not clear whether or not the units match on both sides of the equation, for example when both sides involve derived SI units. In that case, it may be useful to break all the derived units down in terms of base SI units (m, kg, s, A, K, mol, cd).
- https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/Book%3A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)/01%3A_Units_and_Measurement/1.05%3A_Dimensional_AnalysisThe dimension of a physical quantity is just an expression of the base quantities from which it is derived. All equations expressing physical laws or principles must be dimensionally consistent. This ...The dimension of a physical quantity is just an expression of the base quantities from which it is derived. All equations expressing physical laws or principles must be dimensionally consistent. This fact can be used as an aid in remembering physical laws, as a way to check whether claimed relationships between physical quantities are possible, and even to derive new physical laws.
- https://phys.libretexts.org/Courses/Coalinga_College/Physical_Science_for_Educators_(CID%3A_PHYS_14)/02%3A_Units_Measurement_Graphing_and_Calculation/2.08%3A_Measurement/2.8.09%3A_Dimensional_AnalysisDimensional analysis is used in numerical calculations, and in converting units. It can help us identify whether an equation is set up correctly (i.e. the resulting units should be as expected). Units...Dimensional analysis is used in numerical calculations, and in converting units. It can help us identify whether an equation is set up correctly (i.e. the resulting units should be as expected). Units are treated similarly to the associated numerical values, i.e., if a variable in an equation is supposed to be squared, then the associated dimensions are squared, etc.
