Re: Calculate Inertia of a partially hollow sphere

You didn't say what the axis of rotation was to be.

The formula I = 2/3 M R^2 is indeed the formula for inertia for a hollow
sphere, but it is for a sphere with an extremely thin shell.  This seems to 
not
be the case in your problem.


If the axis of rotation is a diameter of the sphere, then we would 
calculate as
follows:


The distance from a point (x,y,z) to the x-axis is y^2 + z^2.

The element of mass is density times the element of volume.

The element of volume is dz dy dx

density is 1/r where r is the distance from the center of the sphere.  

density is 1/sqrt(x^2+y^2+z^2)

Inertia =  8 times  integral of  (y^2 + z^2) / sqrt(x^2 + y^2 + z^2)

as x, y, z each range from R1 to R2.

The reason it is 8 times is because x really goes from -R2 to R1 and from 
R1
to R2.  Similarly, y really goes from -R2 to R1 and from R1 to R2, and z
really goes from -R2 to R1 and from R1 to R2.

If you have additional questions about this answer please
write again to the MadSci Network.

Kermit