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PHY 504
Problem Set #9
due 5 November 2010
1.
Show that
ε
ijk
is invariant under rotations, assuming that it transforms as a 3
index tensor:
ʹ
i
ʹ
j
ʹ
k
=
A
ʹ
i i
A
ʹ
j j
A
ʹ
k k
ijk
2.
A solid rectangular block has sides
a
,
b
, and
c
(a)
Calculate the inertia tensor about one of its corners.
(b)
Find the principal axes and moments.
3.
Derivation 5.7.
4.
A molecule consists of three equalmass atoms located at the corners of a rigid
equilateral triangle of side
a
.
(a)
Calculate the inertia tensor of the molecule about its center of mass, in the
bodyfixed frame.
(b)
Describe the motion of the molecule in the bodyfixed frame, and in
particular find the shape of the polhode. What is the angular frequency of the
precession of the axis of rotation?
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This note was uploaded on 11/16/2010 for the course PHY 504 taught by Professor Staff during the Fall '08 term at Kentucky.
 Fall '08
 Staff
 mechanics

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