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PROBLEM 16.79
In Problem 16.78, determine (a) the distance h for which the horizontal component of the
reaction at A is zero, (b) the corresponding angular acceleration of the rod.
PROBLEM 16.78 A uniform slender rod of length L = 36 in. and weight W = 4 lb hangs
freely from a hinge at A. If a force P of magnitude 1.5 lb is applied at B horizontally to the
left (h = L), determine (a) the angular acceleration of the rod, (b) the components of the
reaction at A.
SOLUTION
L
PROBLEM 16.80
An athlete performs a leg extension on a machine using a 20
kg mass at A located 400 mm away from the knee joint
center O. Biomechanical studies show that the patella
tendon inserts at B, 100 mm below point O and 20 mm from
the center line of the tibia (see figure). The mass of the
lower leg and foot is 5 kg, the CG of this segment is 300
mm from the knee, and the radius of gyration about the knee
is 350 mm. Knowing that the leg is moving at a constant
angular velocity of 30 degrees per second when θ = 60°,
determine (a) the force F in the patella tendon, (b) the
magnitude of the joint force at the knee joint center O.
PROBLEM 16.80 (Continued)
PROBLEM 16.81
The shutter shown was formed by removing one quarter of a disk of
0.75-in. radius and is used to interrupt a beam of light emanating from a
lens at C. Knowing that the shutter weighs 0.125 lb and rotates at the
constant rate of 24 cycles per second, determine the magnitude of the
force exerted by the shutter on the shaft at A.
SOLUTION
See inside front cover for centroid of a circular sector.
3
4
3
4
2
2 sin
3
2(0.75 in.)sin ( )
3( )
0.15005 in.
r
r
r
r
a
a
π
π
=
=
=
PROBLEM 16.82
A 6-in.-diameter hole is cut as shown in a thin disk of 15-in.-diameter. The disk
rotates in a horizontal plane about its geometric center A at the constant rate of
480 rpm. Knowing that the disk has a mass of 60 lb after the hole has been cut,
determine the horizontal component of the force exerted by the shaft on the
disk at A.
SOLUTION
Determination of mass center of disk
We determine the centroid of the composite area:
PROBLEM 16.83
A turbine disk of mass 26 kg rotates at a constant rate of 9600 rpm. Knowing
that the mass center of the disk coincides with the center of rotation O,
determine the reaction at O immediately after a single blade at A, of mass
45 g, becomes loose and is thrown off.
SOLUTION
2
9600 rpm 60
π
ω
=
PROBLEM 16.84
A uniform rod of length L and mass m is supported as shown. If
the cable attached at end B suddenly breaks, determine (a) the
acceleration of end B, (b) the reaction at the pin support.
SOLUTION
02
L
wa
a
= =
eff
( ): 22
AA
LL
M M W I ma
a
Σ=Σ =+
2
1
2 12 2 2
L LL
mg mL m
aa
= +
2
13
23 2
Lg
mg mL L
aa
= =
(b) Reaction at A.
eff
( ): 2
yy
L
F F A mg ma m
a
Σ=Σ − =− =−
3
22
3
4
Lg
A mg m L
A mg mg
−=−
−=−
1
4
A mg=
1
4mg=A
(a) Acceleration of B.
/
0
B n BA
L
a
=+=+a aa
33
22
B
g
Lg
L
= =
a
3
2
Bg=a
PROBLEM 16.85
A uniform rod of length L and mass m is supported as shown. If
the cable attached at end B suddenly breaks, determine (a) the
acceleration of end B, (b) the reaction at the pin support.
SOLUTION
L
47 7
L
7
PROBLEM 16.86
An adapted launcher uses a torsional spring about
point O to help people with mobility impairments
throw a Frisbee. Just after the Frisbee leaves the
arm, the angular velocity of the throwing arm is
200 rad/s and its acceleration is 10 rad/s2, both
counterclockwise. The rotation point O is located
1 in. from the two sides. Assume that you can
model the 2-lb throwing arm as a uniform
rectangle. Just after the Frisbee leaves the arm,
determine (a) the moment about O caused by the
spring, (b) the forces on the pin at O.
PROBLEM 16.87
A 1.5-kg slender rod is welded to a 5-kg uniform disk as shown. The
assembly swings freely about C in a vertical plane. Knowing that in the
position shown the assembly has an angular velocity of 10 rad/s
clockwise, determine (a) the angular acceleration of the assembly,
(b) the components of the reaction at C.
PROBLEM 16.87 (Continued)
(b) Components of reaction of C.
2
y
y
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.
SOLUTION
PROBLEM 16.88 (Continued)
(4 lb)(0.25 ft) (1 ft)(sin 30 )Σ= − °
MT
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.
SOLUTION
32.2 32.2
PROBLEM 16.89 (Continued)
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.
SOLUTION
(a) Angular acceleration.
2
1
PROBLEM 16.90 (Continued)
2
1()
I m CB=
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.
SOLUTION
We first consider the entire system and express that the external forces are equivalent to the inertial terms of
PROBLEM 16.91 (Continued)
(b) Consider now the disk alone:
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
