# Moment of inertia for a hollow ball calculation

1. Feb 27, 2012

### AaronKnight

1. The problem statement, all variables and given/known data
A uniform solid sphere of mass m and radius a has moment of inertia 2/5ma2 about any
diameter. Material is removed from the sphere to make a concentric spherical cavity of
radius a/2. What is the mass of the resulting hollow ball ? Show that its moment of inertia
(31/80)ma2
What does it mean that moments of inertia are additive and why are they so ?

2. Relevant equations
I have calculated the mass of the hollow ball to be (7/6)πρa3

3. The attempt at a solution
I've been attempting to solve this question by calculating the moment of inertia of the material removed from the the sphere and subtracting that from the moment of inertia given for a solid sphere, but this approach doesn't give me the correct coefficient of 31/80, I've checked my maths many times. I am just wondering if this is the correct way of doing this problem?

2. Feb 27, 2012

### fluidistic

I wish I had time to actually help you in details for your problem... however may I point that you should give the mass of the resulting hollow ball in terms of m only, no rho the density.
Huge hint: The ratio of the volume of the sphere and hollow ball is equal to the ration of their mass.

3. Feb 28, 2012

### AaronKnight

Thank you, I think I have managed to solve it now.

4. Feb 28, 2012

### SammyS

Staff Emeritus
Notice that the result for the moment of inertia, (31/80)ma2, is in terms of the mass, m, of the solid sphere, before it is hollowed out.