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PROBLEM 16.87 (Continued)
(b) Components of reaction of C.
2
eff
( ) : (1.5 kg)(14 m/s )
x x x AB n
F F C maΣ=Σ =− =−
PROBLEM 16.88
Two identical 4-lb slender rods AB and BC are
connected by a pin at B and by the cord AC. The
assembly rotates in a vertical plane under the combined
effect of gravity and a
6 lb ft⋅
couple M applied to rod
AB. Knowing that in the position shown the angular
velocity of the assembly is zero, determine (a) the
angular acceleration of the assembly, (b) the tension in
cord AC.
PROBLEM 16.88 (Continued)
(4 lb)(0.25 ft) (1 ft)(sin30 )Σ= − °
B
MT
2
22
1 4 lb 4 lb
(1 ft) (1.25 ft)(0.25 ft)
12 32.2 ft/s 32.2 ft/s
aa
= +
2
4 lb (0.5 ft)(cos.30 )(0.433 ft)
32.2 ft/s
a
+°
0.07246 (0.07246)(3.7154) 1 (0.5) 0.26922T
a
= = =−=
1.462 lbT=
or
1.462 lbT=
PROBLEM 16.89
The object ABC consists of two slender rods welded together at Point B. Rod AB has a
weight of 2 lb and bar BC has a weight of 4 lb. Knowing the magnitude of the angular
velocity of ABC is 10 rad/s when
0,
θ
=
determine the components of the reaction at
Point C at this location.
PROBLEM 16.89 (Continued)
x
FΣ=
eff
( ):
x
FΣ
()cos ()sin ()
x AB AB t AB AB n BC BC t
Cma ma ma
ββ
=++
2
2
( cos sin )
24
(2.0616)(2.3cos14.035 10 sin14.035 ) (1)(2.3)
32.2 32.2
3.6770 lb
AB CD BC CE
mr mr
a βω β a
= ++
= °+ ° +
=
y
FΣ=
eff
( ):
y
FΣ
()sin ()cos ()
y AB BC AB AB t AB AB n BC BC n
Cmgmg ma ma ma
ββ
−−=− + +
2
2
2
( ) ( cos sin )
2
6 (2.0616)(10 cos14.035 2.3sin14.035 )
32.2
4(1)(10)
32.2
30.773 lb
y AB BC AB CD BC CE
y
y
C W W mr mr
C
C
ω βa β ω
=++ − +
= + °− °
+
=
22
30.992 lb
=
30.773
tan 3.6770
83.186
φ
φ
=
= °
31.0 lb=C
83.2°
PROBLEM 16.90
A 3.5-kg slender rod AB and a 2-kg slender rod BC are connected
by a pin at B and by the cord AC. The assembly can rotate in a
vertical plane under the combined effect of gravity and a couple M
applied to rod BC. Knowing that in the position shown the angular
velocity of the assembly is zero and the tension in cord AC is equal
to 25 N, determine (a) the angular acceleration of the assembly,
(b) the magnitude of the couple M.
PROBLEM 16.90 (Continued)
Kinetics:
2
2
2
1()
12
1(2 kg)(0.5 m)
12
0.041667 kg m
BC BC
I m CB=
=
= ⋅
10.13 N m= ⋅M
(0.2 m)
BC C
Mmg I
a
−=
2
22
1
3
CB AB
PROBLEM 16.91
A 9-kg uniform disk is attached to the 5-kg slender rod AB by means of
frictionless pins at B and C. The assembly rotates in a vertical plane under the
combined effect of gravity and of a couple M which is applied to rod AB.
Knowing that at the instant shown the assembly has an angular velocity of 6
rad/s and an angular acceleration of 25 rad/s2, both counterclockwise,
determine (a) the couple M, (b) the force exerted by pin C on member AB.
PROBLEM 16.91 (Continued)
( ) : (0.15) (0.18)(25)
MM C I
a
Σ=Σ = =
PROBLEM 16.92
Derive the equation
CC
MI
a
Σ=
for the rolling disk of Figure 16.17, where
C
MΣ
represents the sum of the
moments of the external forces about the instantaneous center C, and
C
I
is the moment of inertia of the disk
about C.
CC
