# Hollow cube - moment of inertia

#### blr

1. Homework Statement
How to calculate moment of inertia of hollow cube.

2. Homework Equations

3. The Attempt at a Solution
I guess that subtracting the moment of inertia of the inner cube from the moment of inertia of the outer cube is wrong.
Even it is close to solution, what mass to put in formula?

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#### Delphi51

Homework Helper
A good idea to subtract away the inner cube!
The mass of the hollow cube will appear in your answer; if you don't know it just leave it as m.

#### blr

I know mass of hollow cube, and it is m...
Moment of inertia of cube is m a^2/6.
So moment of inertia of hollow cube is m1 a^2/6 - m2 b^2/6....
I need help with m1 and m2...

#### Carid

The density of the initial solid cube is a constant, so the mass is proportional to the volume. The volume of the removed cube and the volume of the remaining cubic shell are calculable in terms of a and b.

#### blr

I know that, but I don't know how to do it :(

#### Borek

Mentor
What is volume of the cube with an edge length a?

??? a^3

#### Borek

Mentor
Good. What is its mass (assuming density d)?

d a^3

#### Borek

Mentor
So where is the problem?

#### blr

So...
I(of hollow cube) = m * $$\frac{a^3}{a^3-b^3}$$ * $$\frac{a^2}{6}$$ - m * $$\frac{b^3}{a^3-b^3}$$ * $$\frac{b^2}{6}$$

that is

$$\frac{m(a^5-b^5)}{6(a^3-b^3}$$

Is that ok?

anyone?

#### Borek

Mentor
I don't get it. What is ma^3/(a^3-b^3)?

#### blr

Mass of hollow cube is given. So that is mass of full cube, before removing inner cube with edge length b.

#### Borek

Mentor
Ah, OK.

Looks OK to me, but I made so many stupid mistakes lately that I don't trust myself these days.

Thank you...