How to Use Dimensional Analysis

Rate: (2 Ratings)

Dimensional analysis is a powerful tool for analyzing equations and easily solving complicated problems. Once you master dimensional analysis you will be able to write out equations, test if the equations are written correctly and solve the problem.

Flag Article

Instructions

Difficulty: Moderately Easy

Things You’ll Need:

Paper
Pencil
Conversions
Calculator

Step1

Understand what units are and how they cancel. A unit is just the category. If you have 15 candy bars, the units are in candy bars. When a unit is divided by a like unit they cancel each other out; draw a line through canceled units.

Step2

Analyze your problem. Determine what units are involved and what units the answer should be in. For example, if you have the problem “A vehicle is moving at 15 meters per second, how far does it travel in 30 seconds?” you want your answer to be in meters.

Step3

Check to see if you need any conversions. Conversions are properties like 2.54 cm per 1 inch, or 12 eggs per 1 carton. If you don’t have the conversions you need memorized already, you can look them up in almost any science text book, or you can find them online.

Step4

Figure 1.1 Set up the equation with just the units. Arrange it so that the units you don’t want cancel and the unit you want the answer to be in is left, like in Figure 1.1.

Step5

Figure 1.2 After you make sure the equation is written correctly, substitute the values in to it, multiply the top values, multiple the bottom values, and then divide the top by the bottom as shown in Figure 1.2.

Step6

Figure 1.3 Break up more complex problems into smaller problems. If you have a problem like, “A bored traffic officer measures the speed of a car to be 113 km per hour and decides to find out how fast it was going in inches per seconds, what value did he get?” you can break that into two equations like in Figure 1.3, where you convert the first value to the desired units and then convert the second value to the desired units. In the problem above we change it to inches per hour, and then we solve for inches per second.