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67. (a) We use conservation of mechanical energy to find an expression for
ω
2
as a
function of the angle
θ
that the chimney makes with the vertical. The potential energy of
the chimney is given by
U = Mgh
, where
M
is its mass and
h
is the altitude of its center
of mass above the ground. When the chimney makes the angle
with the vertical,
h
=
(
H
/2) cos
. Initially the potential energy is
U
i
= Mg
(
H
/2) and the kinetic energy is zero.
The kinetic energy is
1
2
2
I
when the chimney makes the angle
with the vertical, where
I
is its rotational inertia about its bottom edge. Conservation of energy then leads to
MgH
Mg H
I
MgH I
/
( /)
/)
(
22
1
2
=+
¡
=−
cos
1
2
(c
o
s
)
.
2
θω
ω
I = MH
2
/3 (found using Table
102(e) with the parallel axis theorem). Thus
2
33
(
9
.
8
0
m
/
s
)
(1 cos )
(1 cos35.0 )
0.311 rad/s.
55.0 m
g
H
ωθ
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This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics, Energy, Mass, Potential Energy

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