PROBLEM 18.100
An experimental Fresnel-lens solar-energy concentrator can rotate
about the horizontal axis AB, which passes through its mass center
G. It is supported at A and B by a steel framework, which can rotate
about the vertical y axis. The concentrator has a mass of 30 Mg, a
radius of gyration of 12 m about its axis of symmetry CD, and a
radius of gyration of 10 m about any transverse axis through G.
Knowing that the angular velocities
1
and
2
have constant
magnitudes equal to 0.20 rad/s and 0.25 rad/s, respectively, determine
for the position
60
(a) the forces exerted on the concentrator at
A and B, (b) the couple
2
Mk
applied to the concentrator at that
instant.
PROBLEM 18.100 (Continued)
Let the reference frame
xyz
G
be turning with angular velocity
Ωω
eff / / 2
(): ( ) )
BBABxyGB G
AB M MM r ijrWkH
32
62
32 ( ) 16 ( 294.3 10 )
( 32 4.7088 10 ) 32
xy G
yxG
AA M
AAM
kijk jkH
ijkH
PROBLEM 18.100 (Continued)
Equate like components:
63
: 32 4.7088 10 117 10
y
A i 3
143.5 10 N
y
A
3
: 32 57.158 10
x
Aj
3
1.786 10 N
x
A
PROBLEM 18.101
A 6-lb homogeneous disk of radius 3 in. spins as shown at the
constant rate
1
60
rad/s. The disk is supported by the fork-
ended rod AB, which is welded to the vertical shaft CBD. The
system is at rest when a couple
0
(0.25 ft lb)Mj
is applied to
the shaft for 2 s and then removed. Determine the dynamic
reactions at C and D after the couple has been removed.
PROBLEM 18.101 (Continued)
/
DDAAD
m
MHHr a
242
22
02
1
:4
Mmrc
j (1)
11
mm
11
5 in. 0.41667 ft, 60 rad/s, 0
c
While the couple is applied, 00.25 ft lbM
Rearranging Equation (1)
2
0
0.25 7.0899 rad/s
M
At 2s,t
2202
( ) 0 (7.0899)(2) 14.18 rad/st
For 2s,t 02
0, 0M
32.2
62
32.2
(2)(0.33333)
1(0.25) (60)(14.1798) 0 7.4312 lb
(2)(0.333
z
C
33) 2
(7.81lb) (7.43 lb) Cik
PROBLEM 18.102
A 6-lb homogeneous disk of radius 3 in. spins as shown at the
constant rate
1
60
rad/s. The disk is supported by the fork-
ended rod AB, which is welded to the vertical shaft CBD. The
system is at rest when a couple
0
M
is applied as shown to the
shaft for 3 s and then removed. Knowing that the maximum
angular velocity reached by the shaft is 18 rad/s, determine
(a) the couple
0
,M
(b) the dynamic reactions at C and D after
the couple has been removed.
PROBLEM 18.102 (Continued)
/
DDAAD
m
MHHr a
242
22
02
1
:4
Mmrc
j (1)
11
mm
11
5 in. 0.41667 ft, 60 rad/s, 0
c
(a) While the couple is applied 2
2
218 6rad/s
3t
1
PROBLEM 18.103
A 2.5 kg homogeneous disk of radius 80 mm rotates with an
angular velocity
1
with respect to arm ABC, which is welded
to a shaft DCE rotating as shown at the constant rate
2
12
rad/s. Friction in the bearing at A causes
1
to
decrease at the rate of
2
15 rad/s .
Determine the dynamic
reactions at D and E at a time when
1
has decreased to
50 rad/s.
PROBLEM 18.103 (Continued)
Resolve into components.
2
22
2
22
()
()
xx
yy
DEmc b
DEmb c
1
2222
11
ll
mm
ll
Data:
2.5 kg, 80 mm 0.08 m
120 mm 0.12 m, 60 mm 0.06 m, 150 mm 0.15 m
mr
bcl
(2)(0.15) 2
x
D
(22.0 N) (26.8 N) Dij
22
2.5 1 (0.08) ( 15) 0 (0.12)(0.15)(12) 21.2 N
(2)(0.15) 2
E
(21.2 N) (5.20 N) Eij
PROBLEM 18.104
A 2.5-kg homogeneous disk of radius 80 mm rotates at the
constant rate
1
50
rad/s with respect to arm ABC, which is
welded to a shaft DCE. Knowing that at the instant shown shaft
DCE has an angular velocity
2
(12 rad/s)k and an angular
acceleration
2
2
(8 rad/s ) ,
k
determine (a) the couple which
must be applied to shaft DCE to produce that acceleration,
(b) the corresponding dynamic reactions at D and E.