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Dimensional Analysis

Dimensional Analysis

Author: Dixie Gautreaux
Description:

Students will learn the basic steps to dimensional analysis.

In physics, dimension is used to refer to the physical nature of a quantity and the type of unit used to specify it. —The three physical dimensions most commonly used in physics are length, mass, and time. —Dimensional analysis is used to check mathematical relations for the consistency of their dimensions.

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Tutorial


Physics experiments involve the measurement of a variety of quantities. —These measurements should be accurate and reproducible. —The first step in ensuring accuracy and reproducibility is defining the units in which the measurements are made.—


The units for length, mass, and time (as well as a few others), are regarded as base SI units. —These units are used in combination to define additional units for other important physical quantities such as force and energy.—
Since any quantity can be measured in several different units it is CRUCIAL to know how to convert from one to another.  Performing conversions or dimensional analysis is at the core of physics.  These simple calculations should become like second nature to you!


Steps for conversion problems:
1. In all calculations, write down the units EVERYTIME! 
2. Treat all units as algebraic quantities. When identical units are divided, they are eliminated algebraically. 
3. Use the conversion factors located on the page facing the inside cover. Be guided by the fact that multiplying or dividing an equation by a factor of 1does not alter the equation. 

—In physics, dimension is used to refer to the physical nature of a quantity and the type of unit used to specify it. —The three physical dimensions most commonly used in physics are length, mass, and time. —Dimensional analysis is used to check mathematical relations for the consistency of their dimensions.


 

Dimensional Analysis Example

Dimensional Analysis Example - Compound Units