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PROBLEM 18.132
A homogeneous rectangular plate of mass m and sides c and 2c
is held at A and B by a fork-ended shaft of negligible mass which
is supported by a bearing at C. The plate is free to rotate about
AB, and the shaft is free to rotate about a horizontal axis through
C. Initially the plate lies in the plane of the fork 0
(0)
and the
shaft has an angular velocity 010
rad/s. If the plate is slightly
disturbed, determine for the ensuring motion (a) the minimum
value of ,
(b) the maximum value of .
PROBLEM 18.132 (Continued)
Using the initial conditions, including 00,
Eq. (3) yields
(4)
2
max 4.47 rad/s
PROBLEM 18.133
A homogeneous square plate of mass m and side c is held at points A
and B by a frame of negligible mass which is supported by bearings at
points C and D. The plate is free to rotate about AB, and the frame is
free to rotate about the vertical CD. Knowing that, initially, 045 ,
00,
and 08
rad/s, determine for the ensuing motion (a) the
range of values of ,
(b) the minimum value of ,
(c) the maximum
value of .
12
y
PROBLEM 18.133 (Continued)
22
21 20 10
CC C C
(a) 22
144
96 12 96 0
1cos
2
cos 0.5 cos 0.70711
(b) min 12 6 rad/s
1cos0
min 6.00 rad/s
22
max 4.90 rad/s
PROBLEM 18.134
A homogeneous square plate of mass m and side c is held at points A
and B by a frame of negligible mass which is supported by bearings at
points C and D. The plate is free to rotate about AB, and the frame is
free to rotate about the vertical CD. Initially the plate lies in the plane
of the frame
090
and the frame has an angular velocity 08
rad/s. If the plate is slightly disturbed, determine for the ensuing
motion (a) the minimum value of ,
(b) the maximum value of .
12
y
PROBLEM 18.134 (Continued)
22
21 20 10
CC C C
PROBLEM 18.135
A homogeneous disk of radius 9 in. is welded to a rod AG of length 18 in.
and of negligible weight which is connected by a clevis to a vertical shaft
AB. The rod and disk can rotate freely about a horizontal axis AC, and
shaft AB can rotate freely about a vertical axis. Initially rod AG is
horizontal
090
and has no angular velocity about AC. Knowing
that the maximum value m
of the angular velocity of shaft AB in the
ensuing motion is twice its initial value 0,
determine (a) the minimum
value of ,
(b) the initial angular velocity 0
of shaft AB.
PROBLEM 18.135 (Continued)
Conservation of energy: ,TV E
where E is a constant.
22 2 2 22
17 1
(2)
30
mm m
41.2
m
0
2.1250 1.5055ma mga
PROBLEM 18.136
A homogeneous disk of radius 9 in. is welded to a rod AG of length 18 in.
and of negligible weight which is connected by a clevis to a vertical shaft
AB. The rod and disk can rotate freely about a horizontal axis AC, and
shaft AB can rotate freely about a vertical axis. Initially rod AG is
horizontal
090
and has no angular velocity about AC. Knowing
that the smallest value of
in the ensuing motion is 30 , determine
(a) the initial angular velocity of shaft AB, (b) its maximum angular
velocity.
PROBLEM 18.136 (Continued)
Conservation of energy: ,TV E
where E is a constant.
22 2 2 22
17 1
(2)
z
(a) At 30 and at 90 , 0.
mo
17 1 17
00
84
222
17 3 68 17 2 cos30
2
032.2
0.41660 0.41660 17.886
0.75
g
a
04.23 rad/s
(b)
23
m
12.50 rad/s
m
