Moment of Inertia: Solid vs Hollow Disk on Incline

[Invictus1017]

Homework Statement

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 similar to this:
http://youtube.com/watch?v=7mxV6f5nuJY

Homework Equations

I = MR ?

The Attempt at a Solution

Something do with moment of inertia i think.

Thanks a lot.

 

[Hootenanny]

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?

 

[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?

 

[Hootenanny]

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?

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?