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55. (a) The period of the pendulum is given by
TI
m
g
d
=
2
π
/
, where
I
is its rotational
inertia,
m
= 22.1 g is its mass, and
d
is the distance from the center of mass to the pivot
point. The rotational inertia of a rod pivoted at its center is
mL
2
/12 with
L
= 2.20 m.
According to the parallelaxis theorem, its rotational inertia when it is pivoted a distance
d
from the center is
I
=
mL
2
/12 +
md
2
. Thus,
T
mL
d
mgd
Ld
gd
=
+
=
+
2
12
2
12
12
22
2
2
ππ
(/
)
.
Minimizing
T
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics, Center Of Mass, Inertia, Mass

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