Moment of inertia of a thin spherical shell

[abinxur]

Can anyone help me how to calculate the moment of inertia of a thin spherical shell? Thank you

 

[Hootenanny]

Welcome to PF,

One is expected to show some effort in solving before asking for help. However, I will offer you a hint: A spherical shell can be built up by summing up the moments of inertia for an infinite number of infinitesimally small hoops.

 

[tseryan]

The parallel axis theorem helps in calculating moments of inertia of homogeneous rigid bodies with strange geometries. The general equation is:

I (moment of inertia) = Icm + MD^2

In the case of a thin spherical shell it is:

Icm=(2/3)M(R^2)

The "cm" is in subscript by the way. Icm is the moment of inertia about an axis through the center of mass. R is the distance from the center of mass. Hope this helps!