PROBLEM 18.104 (Continued)
Resolve into components.
2
22
2
22
()
()
xx
yy
DEmc b
DEmb c
1
(2)(0.15) 2
y
D
(21.0 N) (28.0 N) Dij
2
2.5 [ 0 (0.06)(0.15)(8) (0.12)(0.15)(12) ] 21.0 N
(2)(0.15) 2
4.00 N
E
(21.0 N) (4.00 N) Eij
PROBLEM 18.105
For the disk of Problem 18.99, determine (a) the couple M1j
which should be applied to arm ABC to give it an angular
acceleration 2
1(7.5 rad/s )
j
when 15 rad/s,
knowing that
the disk rotates at the constant rate 215 rad/s,
(b) the force-
couple system representing the dynamic reaction at A at that
instant. Assume that ABC has a negligible mass.
PROBLEM 18.99 A thin disk of mass 4 kgm
rotates with an
angular velocity 2
with respect to arm ABC, which itself rotates
with an angular velocity 1
about the y axis. Knowing that
5 rad/s and 215 rad/s
and that both are constant,
determine the force-couple system representing the dynamic
reaction at the support at A.
PROBLEM 18.105 (Continued)
Acceleration of Point C.
1/1
( 7.5 ) (0.45 0.225 ) 5 ( 2.25 )
CCA C
ajr jv j i jj k
1
(b) Dynamic reaction.
(45.0 N) (13.50 N) Aik
(6.41 N m) (10.13 N m)
A
Mik
PROBLEM 18.106*
A slender homogeneous rod AB of mass m and length L is made to
rotate at the constant rate
2
about the horizontal z axis, while frame
CD is made to rotate at the constant rate
1
about the y axis. Express as
a function of the angle
(a) the couple M
1
required to maintain the
rotation of the frame, (b) the couple M
2
required to maintain the
rotation of the rod, (c) the dynamic reactions at the supports C and D.
PROBLEM 18.106* (Continued)
22
12 12
22 2
11
cos 2 sin 2
12 12
11
mL mL
ij
1
24 mL
Equivalence of external and effective forces.
Equating the moments of the variable couples:
12
22
1
1sin2
24
G
LC M M
mL
jk j kH
k
Equating the coefficients of the unit vectors:
2
1
1
112
12
22
21
1
:sin2
24
MmL
k
PROBLEM 18.106* (Continued)
1sin 2
PROBLEM 18.107
A uniform thin disk of 6-in. diameter is attached to the end of a rod AB
of negligible mass which is supported by a ball-and-socket joint at
point A. Knowing that the disk is observed to precess about the vertical
axis AC at the constant rate of 36 rpm in the sense indicated and that
its axis of symmetry AB forms an angle 60
with AC, determine
the rate at which the disk spins about rod AB.
PROBLEM 18.107 (Continued)
2
22
10.25 0.03125 ft
22
Ir
m
PROBLEM 18.108
A uniform thin disk of 6-in. diameter is attached to the end of a rod AB
of negligible mass which is supported by a ball-and-socket joint at
point A. Knowing that the disk is spinning about its axis of symmetry
AB at the rate of 2100 rpm in the sense indicated and that AB forms an
angle 45
with the vertical axis AC, determine the two possible
rates of steady precession of the disk about the axis AC.
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
PROBLEM 18.108 (Continued)
2
22
10.25 0.03125 ft
22
Ir
m
22
22 2
11
Irc
58.8 rpm, 35.5 rpm