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108. (a) The angular speed
ω
associated with Earth’s spin is
= 2
π
/
T
, where
T
= 86400s
(one day). Thus,
5
2
7.3 10 rad/s
86400 s
−
π
==
×
and the angular acceleration
α
required to accelerate the Earth from rest to
in one day
is
=
/
T
. The torque needed is then
37
2
5
28
(9.7 10 kg m )(7.3 10 rad/s)
8.2 10 N m
86400s
I
I
T
τα
−
×⋅
×
=
=×
⋅
where we used
()
(
)
2
22
46
3
7
2
5.98 10
kg 6.37 10 m
9.7 10
kg m
55
IM
R
×
×=
×
⋅
for Earth’s rotational inertia.
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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, Acceleration

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