p11_097.pdf

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97. The parallel axis theorem gives
I
=
I
com
+
M h
2
for the rotational inertia about any axis (parallel to the
axis used to compute
I
com
). Let us assume that an axis has already been chosen through the center of
mass of the body such that
I
com
is as small as it possibly can be. Since
M h
2
>
for all nonzero values of
h,
then
I > I
com
from the parallel axis theorem as long as
h
= 0. Thus, with
h
= 0 we get
I
=
I
com
and
therefore the smallest possible value of rotational inertia.

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