What is dimensional analysis and how do you use it?
http://www.alysion.org/dimensional/fun.htm
http://www.chem.tamu.edu/class/fyp/mathrev/mr-da.html
thank you! im still somewhat confused, though.
What specifically confuses you?
Dimensional analysis is a method used in physics and engineering to analyze and solve problems involving physical quantities. It involves considering the dimensions (units) of the quantities involved, rather than their specific numerical values. By manipulating and canceling units, dimensional analysis can be used to check the correctness of equations and derive relationships between different physical quantities.
To use dimensional analysis, you can follow these steps:
1. Identify the known and unknown quantities in the problem. These quantities should have units associated with them.
2. List the relevant physical quantities and their dimensions. For example, the dimension of length is [L], time is [T], and mass is [M].
3. Express the given information and unknown quantity in terms of their dimensions. If a length is given as 5 meters, you would write it as [L] = 5.
4. Formulate an equation that relates the known and unknown quantities. This equation should have equal dimensions on both sides. If you're unsure how to formulate the equation, consider using fundamental equations or known relationships between physical quantities.
5. Manipulate the equation algebraically, using the dimensions of the quantities. Cancel out the dimensions on both sides of the equation and rearrange as necessary. This will allow you to solve for the unknown quantity.
6. Perform the necessary calculations, substituting the numerical values and leaving only the dimensions. Make sure to use consistent units throughout.
7. Check the units of the final answer. If the units are correct, it is likely that the answer is also correct. If the units are not consistent, you may have made an error in your calculations or formulation of the equation.
Remember, dimensional analysis is a powerful tool for checking the correctness of your work and ensuring that the units in your calculations are consistent. It does not provide you with the actual numerical value of the answer, but it can help catch mistakes and guide your problem-solving process.