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Classical Mechanics, Second Edition, 2nd Edition
book

Classical Mechanics, Second Edition, 2nd Edition

by Tai L. Chow
May 2013
Intermediate to advanced content levelIntermediate to advanced
639 pages
23h 12m
English
CRC Press
Content preview from Classical Mechanics, Second Edition, 2nd Edition
357Motion in Non-Inertial Systems
The equation of motion now takes the form
m
r
t
Fmgmr
eff
δ
δ
ω
2
2
2
=+
−×
(11.46)
with
g
eff
given by Equation 11.45. The magnitude of the correction term to
g
resulting from centrifu-
gal force is, for r R,

ωω
ωθ
××=() sin
RR
2
where θ is the co-latitude angle (π/2 – latitude) between
ω
and
rRrR=+
. Now,
ω
π
τ
π
==
×
=
22
24 3600
0731
06
371 00
4
.,
,rad/s, and R 0
0m
.
And we nd that the correction term is quite small:
ω
2
R sin θ = 0.03 sin θ m/s
2
.
The angle α between
g
and
g
eff
is given by
αα≅=ta
n/gg
eff
h
eff
v
where
g
eff
h
and
g
eff
v
are the horizontal and vertical components, respectively, of
g
eff
(using “vertical” ...
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Publisher Resources

ISBN: 9781466569980