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63. We use
A
to denote the length of the stick. Since its center of mass is
A
/2
from
either end, its initial potential energy is
1
2
mg
A
, where
m
is its mass. Its initial kinetic
energy is zero. Its final potential energy is zero, and its final kinetic energy is
1
2
2
I
ω
,
where
I
is its rotational inertia about an axis passing through one end of the stick and
is
the angular velocity just before it hits the floor. Conservation of energy yields

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