<< Chapter < Page Chapter >> Page >

Factoring out like terms

Note that then entire wheel rotates at the same angular velocity, so we can (and did) factor the (1/2) and the w^2 out of the summation equation given above.

Integral calculus is the key

Regardless of how difficult it may seem to you to perform the summation given above, when you complete a course in integral calculus, you will have learnedhow to do that sort of thing for a variety of geometric shapes such as solid cylinders, hollow cylinders, solid spheres, hollow spheres, squares, rectangles,rods, etc. As a result, engineering and physics handbooks contain tables with this sort of information for a variety of common geometrical shapes.

(There is also such a table at (External Link) , but if you are a blind student, your accessibility equipment may not be able to read itreliably.)

The rotational inertia (I)

Getting back to the earlier equation for rotational kinetic energy , the quantity in parentheses cannot change for a given geometric shape. The distance between each mass particle and the axis of rotation staysthe same for a rigid body, and the mass of each mass particle doesn't change. It is conventional to give the quantity in parentheses the symbol I (upper-case"I") and refer to it as either the rotational inertia , or the moment of inertia .

Therefore, using the terminology from the earlier equation for rotational kinetic energy ,

Facts worth remembering -- Rotational Inertia

I = sum from i=0 to i=N(mi*ri^2)

where

  • I represents rotational inertia
  • SI units for rotational inertia are kg*m^2
  • mi represents the ith mass particle in a set of N mass particles
  • ri represents the distance of the ith mass particle from the axis of rotation

Translational versus rotational kinetic energy

Given that information, let's form an analogy between translational kinetic energy from an earlier module and rotational kinetic energy from this module.

Facts worth remembering -- Translational and Rotational Kinetic Energy

Kt = (1/2)*m*v^2

Kr = (1/2)*I*w^2

where

  • Kt represents translational kinetic energy
  • Kr represents rotational kinetic energy
  • m represents mass in kg
  • v represents translational velocity in m/s
  • I represents rotational inertia in kg*m^2
  • w^2 represents angular velocity in radians per second

Comparing the terms

When we compare the terms in the two expressions, we see that angular velocity in one case is analogous to translational velocity in the othercase.

We also see that the rotational inertia in one expression is analogous to the mass in the other expression.

Mass is no longer absolute

As I explained earlier, mass is an absolute in translational terms. The translational inertia depends directly on the amount ofmass.

However, mass is not an absolute in rotational terms. The rotational inertia for rotation depends not only upon the amount of massinvolved, but also on how that mass is geometrically distributed within the object relative to the axis of rotation.

A measure of inertia

In translational terms, mass is a measure of the inertia of an object, or how difficult it is to cause the object to change its translational velocity.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
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
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
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
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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 ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Accessible physics concepts for blind students. OpenStax CNX. Oct 02, 2015 Download for free at https://legacy.cnx.org/content/col11294/1.36
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Accessible physics concepts for blind students' conversation and receive update notifications?

Ask