# Moment of Inertia of Half a Sphere

1. Oct 24, 2012

### theBEAST

1. The problem statement, all variables and given/known data

2. Relevant equations
I_a = I_G + md^2

3. The attempt at a solution
I tried using the parallel axis theorem to find the moment of inertia about the axis.

In the formula sheet they give the moment of inertia of a hemisphere:
I_G = 0.259mr^2, where d, the distance from the center is equal to (3r/8).

Thus to find the inertia about the axis we will have to solve
I_a = 0.259mr^2 + m(3r/8)^2

This ends up giving me 2mr^2/5 which is not the answer... However I still think this is the correct answer. This is because I_a = mr^2/5 = 0.2mr^2 (which is the answer according to the prof) is less than the moment at the center I_G = 0.259mr^2. According to the parallel axis equation I_a = I_G + md^2, I_a must be larger than I_G not smaller...

2. Oct 24, 2012

### ehild

Go back to the definition of the moment of inertia. What is the moment of inertia of a point mass, at distance R from the rotation axis? What if you have two identical point masses at the opposite ends of a diameter?

Your problem is connected to "m". What is it?

ehild

Last edited: Oct 24, 2012