PROBLEM 18.153
A homogeneous disk of weight
6 lb
W
rotates at the constant
rate
1
16 rad/s
with respect to arm ABC, which is welded to
a shaft DCE rotating at the constant rate
2
8 rad/s.
Determine the dynamic reactions at D and E.
PROBLEM 18.153 (Continued)
Resolve into components.
2
22
()
yy
DEmb c
22
2
(2)(1.0) 2
0.186335[0 (1.0)(0.75)(8) 0] 4.47 lb
y
E
PROBLEM 18.154
A 48-kg advertising panel of length
2 2.4 m
a
and width 2b
1.6 m
is
kept rotating at a constant rate
1
about its horizontal axis by a small
electric motor attached at A to frame ACB. This frame itself is kept
rotating at a constant rate
about a vertical axis by a second motor
attached at C to the column CD. Knowing that the panel and the frame
complete a full revolution in 6 s and 12 s, respectively, express, as a
function of the angle
,
the dynamic reaction exerted on column CD by
its support at D.
PROBLEM 18.154 (Continued)
222
12 2
21
cos sin cos
33
mb mb
Mi k
21
12
3
x
22
2
31sin cos
3
z
Mmb
Data: 48 kg, 0.8 mmb
22
2
3
11.23cos N m
x
2
2(48)(0.8) (1.0472)(0.5236)sin cos
3
y
M
1(48)(0.8) (0.5236) sin cos
3
2.81sin cos N m
z
2
(11.23 N m)cos (11.23 N m)sin cos (2.81 N m)sin cos
D
Mi j k
PROBLEM 18.155
A 2500-kg satellite is 2.4 m high and has octagonal bases of sides
1.2 m. The coordinate axes shown are the principal centroidal axes of
inertia of the satellite, and its radii of gyration are
0.90 m
xz
kk
and
0.98 m.
y
k
The satellite is equipped with a main 500-N thruster
E and four 20-N thrusters A, B, C, and D, which can expel fuel in the
positive y direction. The satellite is spinning at the rate of 36 rev/h
about its axis of symmetry ,
y
G which maintains a fixed direction in
space, when thrusters A and B are activated for 2 s. Determine (a) the
precession axis of the satellite, (b) its rate of precession, (c) its rate of
spin.
PROBLEM 18.155 (Continued)
(a) Precession axis:
115.88
x
H
tan
32.788
36
42.327
x
y
Law of sines.
(c)
48.693sin 4.798
sin37.529
6.68 rev/h
PROBLEM 18.156
The space capsule has no angular velocity when the jet at A is activated
for 1 s in a direction parallel to the x axis. Knowing that the capsule
has a mass of 1000 kg, that its radii of gyration are
1.00 m
zy
kk
and
1.25 m,
z
k
and that the jet at A produces a thrust of 50 N,
determine the axis of precession and the rates of precession and spin
after the jet has stopped.
PROBLEM 18.156 (Continued)
Moments of inertia:
222
222
(1000 kg)(1m) 1000 kg m
(1000 kg)(1m) 1000 kg m
xk
yy
Imk
Imk
() 62.5 0.0625 rad/s
1000
() 100 0.0640 rad/s
1562.5
Gx
x
x
Gy
y
y
Gz
z
z
y
yz
I
H
I
H
I
Rates of precession and spin.
Since
,
the precession is retrograde.
PROBLEM 18.157
A homogeneous disk of mass m connected at A and B to a fork-ended shaft of
negligible mass which is supported by a bearing at C. The disk is free to rotate
about its horizontal diameter AB and the shaft is free to rotate about a vertical
axis through C. Initially, the disk lies in a vertical plane
0
(90)
and the shaft
has an angular velocity
08
rad/s. If the disk is slightly disturbed, determine
for the ensuring motion (a) the minimum value of
,
(b) the maximum value of
.
PROBLEM 18.157 (Continued)
Data: 1
2
1
2
e
e
2
1(1 cos 90 )(8)
8 rad/s
8
C