Register to reply

Deriving moment of Inertia

by kuahji
Tags: deriving, inertia, moment
Share this thread:
kuahji
#1
Nov12-09, 05:39 PM
P: 395
I'm attempting to derive the moment of inertia for a cylindrical object.

I know that I=[tex]\int r^2 dm[/tex]

which equals =[tex]\int r^2 p dV[/tex]

My question begins here, the derivations I seen pull p out of the integral, which makes sense to do, because in this case it's a constant. p=M/([tex]\pi[/tex]r^2L). So if I don't pull p out before integrating I get I=Mr^2, if I do pull it out, I get I=M/2r^2. I know the answer should be I=M/2r^2 because I have a solid cylindrical object. So why am I getting a different result when I leave p in, & a different result when I pull p out or am I just making a silly math error?

Below is my work when I leave p inside the integral

I=[tex]\int r^2*p*(2\pi*r)dr[/tex]
=2M[tex]\int r dr[/tex] (replacing p with M/([tex]\pi[/tex]r^2L) before integrating)
=Mr^2
Phys.Org News Partner Science news on Phys.org
World's largest solar boat on Greek prehistoric mission
Google searches hold key to future market crashes
Mineral magic? Common mineral capable of making and breaking bonds
ApexOfDE
#2
Nov12-09, 07:33 PM
ApexOfDE's Avatar
P: 122
I believe that density is constant for each material.

p/s: you replace m = DV, then you replace D = M/V... I dont get it :(
kuahji
#3
Nov12-09, 07:50 PM
P: 395
I replaced dm with pdV & then p with M/V.


Register to reply

Related Discussions
Help Deriving formula for moment of inertia lab Introductory Physics Homework 1
Deriving the moment of inertia for a sphere Calculus & Beyond Homework 4
Deriving Moment of Inertia Introductory Physics Homework 2
Second Moment of Inertia - Area Moment of Inertia Classical Physics 1
What are moment of inertia, mass moment of inertia, and radius of gyration? Introductory Physics Homework 1