
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
eff
given by Equation 11.45. The magnitude of the correction term to
resulting from centrifu-
gal force is, for r ≪ R,
ωω
××=() sin
2
where θ is the co-latitude angle (π/2 – latitude) between
and
. Now,
ω
==
=× =
−
22
24 3600
0731
371 00
4
,rad/s, and R 0
.
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
and
eff
is given by
αα≅=ta
eff
h
eff
v
where
eff
and
eff
are the horizontal and vertical components, respectively, of
eff
(using “vertical” ...