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!