<< Chapter < Page Chapter >> Page >

Examples of rotational inertia

In this section, I will attempt to describe some simple geometric shapes and provide the formula for the rotational inertia for each shape. This informationis largely based on information gleaned from (External Link) .

Terminology

Unless I specify otherwise, the axis of rotation will be the axis of symmetry, such as at the center of a wheel. Also, unless I specify otherwise,

  • r represents the radius
  • m represents the mass

Facts worth remembering -- Examples of rotational inertia

Thin hollow cylindrical shape or hoop

Think of a can of beans without the beans and without the end caps.

I = m*r^2

Solid cylinder or disk

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

Thick-walled cylindrical tube with open ends, of inner radius r1, and outer radius r2

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

Thin rectangular plate of height h and width w with axis of rotation in the center, perpendicular to the plate

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

Solid sphere

I = (2/5)*m*r^2

Then hollow spherical shell

I = (2/3)*m*r^2

Thin rod of length L

Axis of rotation is perpendicular to the end of the rod.

I = (1/3)*m*L^2

Thin rectangular plate of width L and height H

Axis of rotation is along the edge of the plate parallel to the H dimension and perpendicular to the width L.

I = (1/3)*m*L^2

Thin rod of length L

Axis of rotation is through the center of the rod.

I = (1/12)*m*L^2

Thin rectangular plate of width L and height H

Axis of rotation is along the center of the plate parallel to the H dimension perpendicular to the width L.

I = (1/12)*m*L^2

Example scenarios

I will apply some of what we have learned to several different scenarios in this section.

The 2x4 scenario

Returning to the earlier example, pick up an eight-foot piece of 2x4 lumber, grasp it near one end, and try swinging it like a baseball bat.

Then grasp it in the center and rotate it as far as you can without hitting your body.

How does the rotational inertia with the axis at the end compare with the rotational inertia with the axis at the center? What is the ratio of the two?

Solution:

Although this may not be a good approximation, we will use the formulas for a thin rectangular plate of height h and width z from (External Link) . (A 2x4 isn't very thin so this may not be a good approximation.)

When rotated around the end,

Iend = (1/3)*(m*h^2) + (1/12)*(m*z^2)

When rotated around the center,

Icen = (1/12)*(m*h^2 + m*z^2)

where

  • Iend is the rotational inertia with the axis of rotation at the end
  • Icen is the rotational inertia with the axis of rotation at the center
  • m is the mass
  • h is the height
  • z is the width (I avoided the use of w because I have been using that character for angular velocity.)

Define the numeric values

Let h = 96 inches and z = 3.75 inches (a 2x4 really isn't 2 inches thick and 4 inches wide)

Let mass = 1kg. We don't know what the mass of a 2.4 is. However, it will cancel out when we compute the ratio of the two cases. We can use any value solong as we don't ascribe any credibility to the absolute rotational inertia value.

Substitute numeric values for symbols

Questions & Answers

how can chip be made from sand
Eke Reply
is this allso about nanoscale material
Almas
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
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....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
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
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
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
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
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
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




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