Hollow cube - moment of inertia

[blr]

Homework Statement

How to calculate moment of inertia of hollow cube.

Homework Equations

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?

 

[Delphi51]

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 :(
Thanks for your answers!

 

[Borek]

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

 

[blr]

? a^3

 

[Borek]

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

 

[blr]

d a^3

 

[Borek]

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?

 

[blr]

anyone?

 

[Borek]

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]

Ah, OK.

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

 

[blr]

Thank you...