Re: MOMENT OF INTERTIA

[Joseph Bellina <jbellina@SAINTMARYS.EDU>]

I don't know if this came up in the previous notes, but let me take a
stab at it.
Rather than thinking of filling the inside of the hoop, thing instead
about taking some of the mass on the rim of the hoop and moving into the
interior.  If the student understands that more mass away from the axis
implies a higher moment, as in the demo of rotating rods with most of the
mass at the ends vs at the middle, then moving some of the mass closer to
the axis has two effects.  First it increases the amount of mass close to
the axis, and second it decreases the amount of mass far from the axis.
The net result is the moment of inertia decreases.  If you move enough
mass to make a uniform disk, have a object with a much lower moment of
inertia than when all the mass is concentrated on the rim.
Does that help, or have I missed the point of your question?

cheers

On Thu, 17 Dec
1998, David Abineri wrote:

> Another question from a high school student:
>
> If one starts with a hoop and thinks about gradually filling in the
> inside of the hoop with mass until it eventually looks like a disk, one
> is certainly increasing the moment of intertia of the object. The effact
> of the above transformation is to produce an object which will roll ever
> faster down a given incline. I can show this easily mathematically but
> is there an intuitive way of explaining why this happens? My students
> understand the mathematics but seem to need a non mathematical argument
> too.
>
> Any help is appreciated.  David Abineri
>
>
> --
>  David Abineri   dabineri@choice.net