Moment of Inertia?

1. Feb 3, 2008

Invictus1017

1. The problem statement, all variables and given/known data
Alright, so say I have a solid wood disk, and a hollowed out disk of equal mass.
I roll them both down an incline, which one gets to the bottom first and why?
The scenario is very similiar to this:

2. Relevant equations
I = MR ?

3. The attempt at a solution
Something do with moment of inertia i think.

Thanks alot.

2. Feb 3, 2008

Hootenanny

Staff Emeritus
As you say, the moment of inertia is a crucial factor. You can answer this question quantitatively that is, explicitly calculate the moment of inertia for each disk and then evaluate it's acceleration. An alternative (and much easier) method would be to use the definition of Moment of Inertia for a point particle (I=mr2 not I=mr as you have above), and logical reasoning.

So to start we know that both their masses are equal, using the definition of I that I gave you above, can you make the next step?

Last edited: Feb 3, 2008
3. Feb 3, 2008

Invictus1017

I'm not sure but, the radius from the center of mass to the axis of the hollow disk is larger than the radius of the solid disk? Resulting in a smaller moment of inertia for the solid disk?

Last edited: Feb 3, 2008
4. Feb 4, 2008

Hootenanny

Staff Emeritus
Well you conclusion is correct, but your reasoning is wrong. The centre of mass of both disc both lie on the axis of rotation. However, the hollow disc has a greater proportion of its mass located further away from the axis of rotation, thus the moment of inertia is greater. Does that make sense?