# 0.32 Phy1320: angular momentum -- the mathematics of torque  (Page 13/13)

 Page 13 / 13

The torque will cause the door to rotate in a counter clockwise direction. Therefore, the torque has a positive sign.

## Torque and the moment of inertia

Three objects are rotating about their centers. All three objects have a mass of 10 kg. The three objects have the followingshapes:

A. A solid disk with a moment of inertia given by

I = (1/2)*m*r^2

where

• r = 2m

B. A disk with a round hole in the center with a moment of inertia given by

I = (1/2)*m*(r1^2 + r2^2)

where

• r1 = 1m
• r2 = 2m

C. A square plate with a moment of inertia given by

I = (1/12)*m*(h^2 + w^2)

where

• h = w = 3.54m

Find the net torque required to cause each object to accelerate at a rate of 10 radians/sec^2.

Solution:

All three solutions are based on the general equation for torque given in Figure 5 .

A. T = I * A, or

T = (1/2)*m*r^2 * A, or

T = (1/2)*10kg*(2m)^2 * 10 radians/second^2

Entering this expression into the Google calculator gives us

T = 200 N*m

B. T = I * A, or

T = (1/2)*m*(r1^2 + r2^2) * A, or

T = (1/2)*10kg*((1m)^2 + (2m)^2) * 10 radians/second^2, or

T = 250 N*m

Note that because more of the mass is located close to the outer edge of the disk, the moment of inertia is higher and more torque is required to achieve thesame acceleration for the same mass.

C. T = I * A, or

T = (1/12)*m*(h^2 + w^2) * A, or

T = (1/12)*10kg*((3.54m)^2 + (3.54m)^2) * 10 radians/second^2, or

T = 2.09 N*m

Note that the square in part C was designed to have the same surface area as the disk in part A. The mass in both cases was uniformly distributed throughoutthe entire surface. Under those conditions, a square has a slightly higher moment of inertia than a disk and thus requires a slightly greater torque toachieve the same acceleration.

## Repeat the computations

I encourage you to repeat the computations that I have presented in this lesson to confirm that you get the same results. Experiment withthe scenarios, making changes, and observing the results of your changes. Make certain that you can explain why your changes behave as they do.

## Resources

I will publish a module containing consolidated links to resources on my Connexions web page and will update and add to the list as additional modulesin this collection are published.

## Miscellaneous

This section contains a variety of miscellaneous information.

Housekeeping material
• Module name: Angular Momentum -- The Mathematics of Torque
• File: Phy1320.htm
• Revised: 10/02/15
• Keywords:
• physics
• accessible
• accessibility
• blind
• graph board
• protractor
• refreshable Braille display
• JavaScript
• trigonometry
• torque
• force
• mass
• angular acceleration
• moment of inertia
• rotational inertia
• vector
Disclaimers:

Financial : Although the openstax CNX site makes it possible for you to download a PDF file for the collection that contains thismodule at no charge, and also makes it possible for you to purchase a pre-printed version of the PDF file, you should beaware that some of the HTML elements in this module may not translate well into PDF.

You also need to know that Prof. Baldwin receives no financial compensation from openstax CNX even if you purchase the PDF version of the collection.

In the past, unknown individuals have copied Prof. Baldwin's modules from cnx.org, converted them to Kindle books, and placed them for sale on Amazon.com showing Prof. Baldwin as the author.Prof. Baldwin neither receives compensation for those sales nor does he know who doesreceive compensation. If you purchase such a book, please be aware that it is a copy of a collection that is freelyavailable on openstax CNX and that it was made and published without the prior knowledge of Prof. Baldwin.

Affiliation : Prof. Baldwin is a professor of Computer Information Technology at Austin Community College in Austin, TX.

-end-

how can chip be made from sand
is this allso about nanoscale material
Almas
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
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
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
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
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
Got questions? Join the online conversation and get instant answers!