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8.8. CHAPTER 8, PROBLEM 8
335
8.8
Chapter 8, Problem 8
Problem:
A projectile of mass
m
has a radius of gyration
R
about its axis of symmetry (
x
axis) and a
radius of gyration
4
R
about the transverse axis (
y
axis). Its angular velocity,
ω
, can be resolved into two
components. The first is the
rate of spin
,
ω
s
, which is directed along the axis of symmetry. The second
is the
rate of precession
,
ω
p
, which is parallel to the projectile’s velocity vector (Axis GD). For the
projectile shown, the angularmomentum vector relative to its center of mass is
H
G
=
H
(
i
−
0
.
032
j
)
,
where
H
is a constant.
(a) Determine
ω
as a function of
H
,
m
and
R
.
(b) Determine
ω
s
and
ω
p
as functions of
H
,
m
,
R
and the angle
θ
between the symmetry axis and
the velocity vector.
HINT:
Let
ω
=
ω
s
i
+
ω
p
p
,whe
re
p
is a unit vector parallel to the velocity
vector.
(c) If the projectile has
R
=5
cm,
m
=30
kg,
H
=0
.
75
kg
·
m
2
/sec and
θ
o
, compute the
projectile’s angularvelocity vector,
ω
=
ω
x
i
+
ω
y
j
, and its spin and precession rates,
ω
s
and
ω
p
,
respectively.
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 '06
 Shiflett

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