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This module is part of a collection of modules intended for students enrolled in a special section of MATH 1508 (PreCalculus) for preengineers. This module addresses the topic of radicals. Radicals play an important role in the modeling of physical phenomena. Several applications of radicals in the field of engineering are presented.



Equations involving radicals abound in the various fields of engineering. Students of engineering must therefore gain confidence and competence in solving equations that include radical expressions. In this module, several different applications that involve the use of radicals to solve engineering problems are presented along with several exercises.

Centripetal force

Centripetal force is the inward directed force that is exerted on one body as it moves in a circular path about another body.

Figure 1 illustrates a body that is in circular motion about a center point.

Centripetal force for an object under rotation.

As the object moves about the circle, its angle changes. This time rate of change of the angle is called the angular velocity and is denoted by the symbol ω. The angular velocity has units of radians/sec. As an example, if the object makes 2 revolutions in a second, it would have an angular velocity

ω = 2 revolutions s = 2 ( 2 π rad ) s = 4 π rad / s size 12{ω= { {2` ital "revolutions"} over {s} } = { {2` \( 2`π` ital "rad" \) } over {s} } =4`π` ital "rad"/s} {}

Examination of Figure 1 shows the centripetal force being directed inward toward the center of the circular path of the object. The velocity of the object is illustrated as being in the direction of the tangent at the point on the circle occupied by the object. If for any reason the body were released from its orbit about the center point, it would travel in a straight line path indicated in the direction of the velocity.

Quite often, one may measure the amount of time that it takes for the object to complete a complete revolution and denote it as the variable ( T ). This value which is usually expressed in seconds is called the period of revolution. For the example given previously where the object makes 2 revolutions per second, the period of revolution ( T ) is ½ second.

The period of revolution ( T ) measured in seconds can be calculated by means of a relationship that involves the magnitude of the centripetal force ( F ) measured in Newtons, the mass of the object ( m ) measured in kilograms, and the radius ( R ) of the circle measured in meters.

T = 4 m R π 2 F size 12{T= sqrt { { {4`m`R`π rSup { size 8{2} } } over {F} } } } {}

Question: A mass of 2 kg revolves about an axis. The radius of the object about the axis is 0.5 m. It takes 0.25 seconds for the mass to make a single revolution. What is the value of the centripetal force?

Solution: We begin by replacing the variables of equation (2) by their numeric values

0 . 25 = 4 ( 2 ) ( 0 . 5 ) π 2 F size 12{0 "." "25"= sqrt { { {4` \( 2 \) ` \( 0 "." 5 \) `π rSup { size 8{2} } } over {F} } } } {}

Next we take the square of each side of the equation

( 0 . 25 ) 2 = 4 π 2 F size 12{ \( 0 "." "25" \) rSup { size 8{2} } = { {4`π rSup { size 8{2} } } over {F} } } {}

We can isolate F on the left hand side of the equation as

F = 4 π 2 0 . 625 size 12{F= { {4`π rSup { size 8{2} } } over {0 "." "625"} } } {}

Which leads to the result F = 632 N . size 12{F="632"`N "." } {}

Nozzle characteristics for aircraft de-icing

The presence of ice on the wings and fuselage on an aircraft can lead to severe problems during stormy winter weather. Equipment is used to spray aircraft with a de-icing agent prior to take-off in order to remove the ice from the wing surfaces and fuselage of planes.

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Can someone give me problems that involes radical expressions like area,volume or motion of pendulum with solution

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Source:  OpenStax, Math 1508 (laboratory) engineering applications of precalculus. OpenStax CNX. Aug 24, 2011 Download for free at http://cnx.org/content/col11337/1.3
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