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HW#6—Solutions
—Phys410—Fall 2011
Prof. Ted Jacobson
Room 4115, (301)4056020
www.physics.umd.edu/grt/taj/410a/
jacobson@umd.edu
9.2 (
artiﬁcial gravity in rotating space station
)
(a) Force of ﬂoor and acceleration both radial inward.
(b) No acceleration, ﬂoor force radial inward, centrifugal force radial outward.
(c)
ω
=
p
g/R
= 0
.
5 rad/s
2
= 4.77 rpm.
(d) Δ
g
eff
/g
eff
= Δ
R/R
= 0
.
05, i.e. 5%.
9.7 (
derivative of vector in rotating frame
) (a) The vector simply rotates along with the
angular velocity of the frame. (b) The vector rotates opposite to
S
in order to remain
constant in
S
0
.
9.8 (
direction of centrifugal and Coriolis forces
)
(a) Moving S near pole: centrifugal S and slightly up, Coriolis W.
(b) Moving E on equator: centrifugal up, Coriolis up.
(c) Moving S across equator: centrifugal up, Coriolis zero.
9.11 (
Lagrangian in rotating frame and equations of motion
)
vector method
: Consider just the kinetic part of the Lagrangian,
L
=
1
2
mv
2
0
. Given
v
0
=
v
+
Ω
×
r
, we have
v
0
·
v
0
=
v
·
v
+ 2
v
·
(Ω
×
r
) + (
Ω
×
r
)
·
(
Ω
×
r
). For
the derivatives with respect to the vector components of
v
and
r
I will use a vector
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 Fall '11
 Jacobson
 mechanics, Acceleration, Force, Gravity

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