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ΔΔ
ω
=
′
−=
′
−=−
′
11
T
T
T
T
.
We can approximate that last denominator as
T
so that we end up with the simple
relationship
ωω
=
TT
. Now, conservation of angular momentum gives us
LI
I
I
==
≈
+
0
b
g
b
g
b
g
so that
=
II
. Thus, using our expectation that rotational inertia is proportional
to the equatorial radius squared (supported by Table 102(f) for a perfect uniform sphere,
but then this isn’t a perfect uniform sphere) we have
()
2
26
230m
2
6.37 10 m
e
e
ee
R
R
TI
R
R
Δ
Δ
≈
=
×
so with
T
= 86400s we find (approximately) that
Δ
T
= 0.8 s. The radius of the earth can
be found in Appendix C or on the inside front cover of the textbook.
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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, Inertia

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