Moment of Inertia of a Sphere derivation?

[Timothy S]

Hi,

Is there a way to derive the moment of inertia of a sphere without using the M of I of a cylinder? In other words, is it possible to find a sphere's from scratch? Please include a derivation in your answer, unless there isn't one of course.

 

[Orodruin]

Why don't you just integrate over the sphere to get it?

 

[Timothy S]

can you explain to me how to do that?

 

[Orodruin]

Do you know the expression for the moment of inertia for an arbitrary object?

 

[Timothy S]

I do, but I don't know how to properly set the equation so that I can integrate.

 

[PeroK]

I do, but I don't know how to properly set the equation so that I can integrate.

Try this:

http://tutorial.math.lamar.edu/Classes/CalcIII/TISphericalCoords.aspx

 

[SteamKing]

Hi,

Is there a way to derive the moment of inertia of a sphere without using the M of I of a cylinder? In other words, is it possible to find a sphere's from scratch? Please include a derivation in your answer, unless there isn't one of course.

Of course there is a way to derive the MOI of a sphere or any other body from scratch. Do you think we make these things up to torture college freshmen?

This article:

http://www.solitaryroad.com/c375.html

contains the general method for calculating mass, the location of centroids, and the mass moment of inertia for a general body.

See Section II - Moments of inertia of masses.