Dimensions of force are [L 1 M 1 T -2 ]. Dimensions of force are [L 2 M 1 T -2 ]. Limitations of Dimensional Analysis:. Change of Fundamental Quantities:. What would be the dimensional equation of mass and density? If velocity V , time T and force F were chosen as fundamental quantities, find dimensions of Mass? If the force F , acceleration A , and time T are taken as fundamental Units, then find the dimensions of energy. Dimensions of energy are [F 1 A -1 T 2 ].
Previous Topic: Dimensions of Physical Quantities. Your email address will not be published. Close Menu About Us. Terms of Service. In [ ]:. Table Of Contents 1. This Page Show Source. Quick search. Powered by Sphinx 1. If either of these rules is violated, an equation is not dimensionally consistent and cannot possibly be a correct statement of physical law. This simple fact can be used to check for typos or algebra mistakes, to help remember the various laws of physics, and even to suggest the form that new laws of physics might take.
This last use of dimensions is beyond the scope of this text, but is something you will undoubtedly learn later in your academic career. Suppose we need the formula for the area of a circle for some computation. But which is which? One natural strategy is to look it up, but this could take time to find information from a reputable source.
It is nice to have a way to double-check just by thinking about it. Also, we might be in a situation in which we cannot look things up such as during a test. Thus, the strategy is to find the dimensions of both expressions by making use of the fact that dimensions follow the rules of algebra. If either expression does not have the same dimensions as area, then it cannot possibly be the correct equation for the area of a circle.
We know the dimension of area is L 2. This may seem like kind of a silly example, but the ideas are very general. As long as we know the dimensions of the individual physical quantities that appear in an equation, we can check to see whether the equation is dimensionally consistent.
On the other hand, knowing that true equations are dimensionally consistent, we can match expressions from our imperfect memories to the quantities for which they might be expressions. Suppose we want the formula for the volume of a sphere. Which one is the volume? By the definition of dimensional consistency, we need to check that each term in a given equation has the same dimensions as the other terms in that equation and that the arguments of any standard mathematical functions are dimensionless.
All three terms have the same dimension, so this equation is dimensionally consistent. The technical term for an equation like this is nonsense. So far, so good.
0コメント