Want to join our mediation workshop that helps you to study better?

The Eduladder is a community of students, teachers, and programmers just interested to make you pass any exams. So we help you to solve your academic and programming questions fast.
In eduladder you can Ask,Answer,Listen,Earn and Download Questions and Question papers.
Watch related videos of your favorite subject.
Connect with students from different parts of the world.
Apply or Post Jobs, Courses ,Internships and Volunteering opportunity. For FREE
See Our team
Wondering how we keep quality?
Got unsolved questions? Ask Questions

Elements-of-Civil-Engineering--Engineering-Mechanics---CV13-OR-CV23-->View question

State and prove parallel axis theorem

Elements of Civil Engineering and engineering mechanics


Asked On2017-06-14 06:38:18 by:Aparna-Dasgupta

Taged users:


Likes:
Be first to like this question

Dislikes:
Be first to dislike this question
Talk about this  Like  Dislike
View all qusetions
Answers

In physics, the parallel axis theorem, also known as Huygens–Steiner theorem, or just as Steiner's theorem, after Christiaan Huygens and Jakob Steiner, can be used to determine the mass moment of inertia or the second moment of area of a rigid body about any axis, given the body's moment of inertia about a parallel axis through the object's center of gravity and the perpendicular distance between the axes.

Derivation:


We may assume, without loss of generality, that in a Cartesian coordinate system the perpendicular distance between the axes lies along the x-axis and that the centre of mass lies at the origin. The moment of inertia relative to the z-axis is
I_{\mathrm {cm} }=\int (x^{2}+y^{2})\,dm.
The moment of inertia relative to the axis z′, which is a perpendicular distance d along the x-axis from the centre of mass, is
{\displaystyle I=\int \left[(x+d)^{2}+y^{2}\right]\,dm}
Expanding the brackets yields
{\displaystyle I=\int (x^{2}+y^{2})\,dm+d^{2}\int dm+2d\int x\,dm.}
The first term is Icm and the second term becomes md2. The integral in the final term is the x-coordinate of the centre of mass, which is zero by construction. So, the equation becomes:
I=I_{\mathrm {cm} }+md^{2}.


Answerd on:2017-06-14 Answerd By:tarun101

Likes:
Be first to like this answer

Dislikes:
Be first to dislike this answer
Talk about this  Like  Dislike

You might like this video:Watch more here

Watch more videos from this user Here

Learn how to upload a video over here



Lets together make the web is a better place

We made eduladder by keeping the ideology of building a supermarket of all the educational material available under one roof. We are doing it with the help of individual contributors like you, interns and employees. So the resources you are looking for can be easily available and accessible also with the freedom of remix reuse and reshare our content under the terms of creative commons license with attribution required close.

You can also contribute to our vision of "Helping student to pass any exams" with these.
Answer a question: You can answer the questions not yet answered in eduladder.How to answer a question
Career: Work or do your internship with us.Work with us
Create a video: You can teach anything and everything each video should be less than five minutes should cover the idea less than five min.How to upload a video on eduladder