Proofing Moment of Inertia Solid Sphere

[chocophysuny]

Homework Statement

Can i use "pyramid" method to derive the equation of Moment Inertia solid sphere?
The pyramid is such we slice a watermelon.
Sorry for my bad english.
Regards.

Homework Equations

2/5 MR^2

The Attempt at a Solution

 

[Sunil Simha]

Hello chocophysuny,
Welcome to Physics Forums,

Can i use "pyramid" method to derive the equation of Moment Inertia solid sphere?

Have you tried it? You must show what you have tried to get help on PF (forum rules).

Sunil

 

[haruspex]

It doesn't seem to me that it would be a useful approach. It does not simplify anything. You need to slice it into elements that have an easily calculated MI, such as discs perpendicular to the axis of rotation.

 

[chocophysuny]

It doesn't seem to me that it would be a useful approach. It does not simplify anything. You need to slice it into elements that have an easily calculated MI, such as discs perpendicular to the axis of rotation.

But my lecture say this method is easy enough to solve.
And, actually i confused to find the element of volume and element of MI.

So, in your opinion, this is not solvable?

 

[chocophysuny]

Hello chocophysuny,
Welcome to Physics Forums,




Have you tried it? You must show what you have tried to get help on PF (forum rules).

Sunil

Yes, I've tried it. But i didn't find the solution.
I'm confused with the element of volume and element of pyramid

"To find MI from the element, we need element of volume and element of MI, isn't it?"

 

[Sunil Simha]

"To find MI from the element, we need element of volume and element of MI, isn't it?"

I'm sorry, I didn't understand what you meant there.

 

[haruspex]

But my lecture say this method is easy enough to solve.
And, actually i confused to find the element of volume and element of MI.

So, in your opinion, this is not solvable?

Maybe I misunderstand the proposed method. From your watermelon analogy, I assumed it involves slicing the sphere into thin wedges using planes through the axis of rotation. If so, I think you would then need to cut each wedge into laminae, either rectangular ones parallel to the axis or triangular ones orthogonal to the axis.