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Re: MOMENT OF INTERTIA



David Abineri <dabineri@CHOICE.NET> writes:
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.

That is perfectly true. So far the student reasoning is perfect.


The effect 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.

Your students should learn that the moment of inertia depends on
something else besides the mass that is rotating. When the
hoop is filled, the radial distance between the average particle
in the filled hoop and the center of rotation decreases.
The smaller distance has more influence on the moment of inertia
than the increase of mass. It not only overcomes the effect of increased
mass but it actually results in an overall decrease of the
moment of inertia.

Analogies are usually poor... but try this one on your students:
On the football field, the heavier team has a greater advantage.
However, if the lighter team is also much faster than the other,
it will win every time.

Herb Gottlieb from New York City
(Where our physics teams are much better than our football teams)