Resource Lesson
Dimensional Analysis
Printer Friendly Version
In physics, the
dimension of a quantity
means its type of measure, not a specific unit of measurement. For example, the volume of an object can be measured in liters, cubic meters, and cubic centimeters. Or, we can talk about volume having a dimension of [L]
^{3}
and not specify any one particular system.
Dimensional analysis
, in which you substitute for each variable in a formula its dimension, is a valuable tool that allows you to check whether the powers, products, and quotients are correct in a formula. It does NOT check for whether the numerical coefficients or +/- signs are correct.
To check a formula for
dimensional consistency
, merely substitute for each variable its appropriate dimension value and simply each term. Remember, that you are not actually adding together "quantities" only their "dimensions."
For example, you have forgotten which of the following formulas is the correct one for relating distance traveled, time interval and rate of speed. Is it d = r/t or t = d/r.
We can use dimensional analysis to determine which version of the formula is correct. For distance, d, we use [L]; for time, t, we use [T]; for rate or speed, r, we use [L]/[T].
Now which one works?
d = r/t
t = d/r
[L] = [L]/[T]/[T]
[L] = [L]/[T]
^{2}
No!
[T] = [L]/[L]/[T]
[T] = [T]
Therefore we now know that the formula t = d/r which can be restated as d = rt is dimensionally consistent.
Two further examples of dimensional analysis proofs follow:
Notice in this example,
(m - m) = m, NOT, 0
Notice in this example,
m + m = m, NOT, 2m.
Related Documents
Lab:
Labs -
2-Meter Stick Readings
Labs -
Acceleration Down an Inclined Plane
Labs -
Addition of Forces
Labs -
Circumference and Diameter
Labs -
Cookie Sale Problem
Labs -
Density of a Paper Clip
Labs -
Determining the Distance to the Moon
Labs -
Determining the Distance to the Sun
Labs -
Eratosthenes' Measure of the Earth's Circumference
Labs -
Force Table - Force Vectors in Equilibrium
Labs -
Home to School
Labs -
Indirect Measurements: Height by Measuring The Length of a Shadow
Labs -
Indirect Measures: Inscribed Circles
Labs -
Inertial Mass
Labs -
Introductory Simple Pendulums
Labs -
Lab: Rectangle Measurements
Labs -
Lab: Triangle Measurements
Labs -
Marble Tube Launcher
Labs -
Quantized Mass
Labs -
The Size of the Moon
Labs -
The Size of the Sun
Labs -
Video Lab: Falling Coffee Filters
Resource Lesson:
RL -
Basic Trigonometry
RL -
Basic Trigonometry Table
RL -
Curve Fitting Patterns
RL -
Linear Regression and Data Analysis Methods
RL -
Metric Prefixes, Scientific Notation, and Conversions
RL -
Metric System Definitions
RL -
Metric Units of Measurement
RL -
Potential Energy Functions
RL -
Properties of Lines
RL -
Properties of Vectors
RL -
Significant Figures and Scientific Notation
RL -
Vector Resultants: Average Velocity
RL -
Vectors and Scalars
Review:
REV -
Honors Review: Waves and Introductory Skills
REV -
Physics I Review: Waves and Introductory Skills
REV -
Test #1: APC Review Sheet
Worksheet:
APP -
Puppy Love
APP -
The Dognapping
APP -
The Pool Game
APP -
War Games
CP -
Inverse Square Relationships
CP -
Sailboats: A Vector Application
CP -
Satellites: Circular and Elliptical
CP -
Tensions and Equilibrium
CP -
Vectors and Components
CP -
Vectors and Resultants
CP -
Vectors and the Parallelogram Rule
WS -
Calculating Vector Resultants
WS -
Circumference vs Diameter Lab Review
WS -
Data Analysis #1
WS -
Data Analysis #2
WS -
Data Analysis #3
WS -
Data Analysis #4
WS -
Data Analysis #5
WS -
Data Analysis #6
WS -
Data Analysis #7
WS -
Data Analysis #8
WS -
Density of a Paper Clip Lab Review
WS -
Dimensional Analysis
WS -
Frames of Reference
WS -
Graphical Relationships and Curve Fitting
WS -
Indirect Measures
WS -
Lab Discussion: Inertial and Gravitational Mass
WS -
Mastery Review: Introductory Labs
WS -
Metric Conversions #1
WS -
Metric Conversions #2
WS -
Metric Conversions #3
WS -
Metric Conversions #4
WS -
Properties of Lines #1
WS -
Properties of Lines #2
WS -
Scientific Notation
WS -
Significant Figures and Scientific Notation
TB -
Working with Vectors
TB -
Working with Vectors
REV -
Math Pretest for Physics I
PhysicsLAB
Copyright © 1997-2022
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton