# 2.5 Game 2302-0350 units and dimensional analysis

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The purpose of this module is to explain units and dimensional analysis.

## General

This module is part of a series of modules designed for teaching the physics component of GAME2302 Mathematical Applications for Game Development at Austin Community College in Austin, TX. (See GAME 2302-0100: Introduction for the first module in the course along with a description of the course,course resources, homework assignments, etc.)

The purpose of this module is to explain units and dimensional analysis.

## Viewing tip

I recommend that you open another copy of this document in a separate browser window and use the following links to easily find and view the Figuresand Listings while you are reading about them.

## General background information

As a young engineering student many years ago, I was told that when evaluating mathematical expressions, I should always embed the units in theexpression, manipulate them algebraically, and confirm that the units that survive until the end of the evaluation are correct relative to the problemspecifications.

Three good reasons

There are at least three good reasons for following this procedure:

• It shows what the units of the result are. A common mistake is to get the correct numerical result of a calculation but to write it with the wrong units.
• It shows where unit conversions must be performed. If units that should have canceled do not cancel, we need to go back and perform the necessary conversions. Forexample, when a speed in miles per hour is being calculated and the result comes out with units of miles per second, we should convert seconds to hours.
• It helps to locate mistakes. If a velocity (meters per second) is being calculated and the units come out as seconds per meter, we know to look for an error.

## Formatting mathematical expressions

Multiple-line format

We might typically write a fraction as a horizontal line with the numerator above the line and the denominator below the line using superscripts to indicateexponents. The product of two fractions would typically be written in the same format with a multiplication indicator joining the two fractions.

Single-line format

Figure 1 shows multiplication and division of fractions in a single-line format similar to how we write expressions incomputer programs.

#### Questions & Answers

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
how did you get the value of 2000N.What calculations are needed to arrive at it
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