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CHAPTER 17
PROBLEM 17.1
A 200-kg flywheel is at rest when a constant 300 N m
couple is applied. After executing 560 revolutions, the
flywheel reaches its rated speed of 2400 rpm. Knowing that the radius of gyration of the flywheel is 400 mm,
determine the average magnitude of the couple due to kinetic friction in the bearing.
f
f
PROBLEM 17.2
The rotor of an electric motor has an angular velocity of 3600 rpm when the load and power are cut off. The
110-lb rotor, which has a centroidal radius of gyration of 9 in., then coasts to rest. Knowing that the kinetic
friction of the rotor produces a couple of magnitude 2.5 lb ft,
determine the number of revolutions that the
rotor executes before coming to rest.
SOLUTION
PROBLEM 17.3
Two uniform disks of the same material are attached to a shaft as shown.
Disk A has a weight of 10 lb and a radius r = 6 in. Disk B is twice as thick as
disk A. Knowing that a couple M of magnitude 22 lb ft is applied to disk A
when the system is at rest, determine the radius nr of disk B if the angular
velocity of the system is to be 480 rpm after 5 revolutions.
2232.212
2
32.2
AA
tr
2
46.5466 1.5996nn
1.5996 6 in. 9.597 in.
BA
rnr
9.60 in.
B
r
PROBLEM 17.4
Two disks of the same material are attached to a shaft as shown. Disk A has
radius r and has a thickness b, while disk B has radius nr and thickness 2b. A
couple M of constant magnitude is applied when the system is at rest and is
removed after the system has executed 2 revolutions. Determine the value of
n which results in the largest final speed for a point on the rim of disk B.
PROBLEM 17.4 (Continued)
Value of n for maximum final speed.
2
dn
PROBLEM 17.5
The flywheel of a small punch rotates at 300 rpm. It is known that 1800 ft lb of work must be done each time a
hole is punched. It is desired that the speed of the flywheel after one punching be not less that 90 percent of the
original speed of 300 rpm. (a) Determine the required moment of inertia of the flywheel. (b) If a constant 25-lb ft
couple is applied to the shaft of the flywheel, determine the number of revolutions which must occur between each
punching, knowing that the initial velocity is to be 300 rpm at the start of each punching.
PROBLEM 17.6
The flywheel of a punching machine has a mass of 300 kg and a radius of gyration of 600 mm. Each punching
operation requires 2500 J of work. (a) Knowing that the speed of the flywheel is 300 rpm just before a
punching, determine the speed immediately after the punching. (b) If a constant 25-N m couple is applied to
the shaft of the flywheel, determine the number of revolutions executed before the speed is again 300 rpm.
SOLUTION
PROBLEM 17.7
Disk A, of weight 10 lb and radius
6r
in., is at rest when it is placed in
contact with belt BC, which moves to the right with a constant speed
40v
ft/s. Knowing that
0.20
k
between the disk and the belt, determine the
number of revolutions executed by the disk before it attains a constant
angular velocity.
2
8 (0.5 ft)(0.20)(32.2 ft/s )
PROBLEM 17.8
The uniform 4-kg cylinder A, of radius r 150 mm, has an angular velocity 0
=
50 rad/s when it is brought into contact with an identical cylinder B which is at rest.
The coefficient of kinetic friction at the contact point D is .
k
After a period of
slipping, the cylinders attain constant angular velocities of equal magnitude and
opposite direction at the same time. Knowing that cylinder A executes three
revolutions before it attains a constant angular velocity and cylinder B executes one
revolution before it attains a constant angular velocity, determine (a) the final
angular velocity of each cylinder, (b) the coefficient of kinetic friction .
k
PROBLEM 17.8 (Continued)
12 5.886 2 36.983 N m
BB k k
Principle of work and energy for cylinder B.
1122
kB
2
0.0225 36.983 0
Bk
(3)
Solving (1), (2), and (3) simultaneously,
22
22
PROBLEM 17.9
The 10-in.-radius brake drum is attached to a larger flywheel which
is not shown. The total mass moment of inertia of the flywheel and
drum is 16 lb
ft
s
2
and the coefficient of kinetic friction between
the drum and the brake shoe is 0.40. Knowing that the initial angular
velocity is 240 rpm clockwise, determine the force which must be
exerted by the hydraulic cylinder if the system is to stop in 75
revolutions.
1122
5053 392.7 0F
12.868 lbF
: 12.868 (0.40)
k
FN N
32.17 lbN
A
83.64 lb
B
PROBLEM 17.10
Solve Problem 17.9, assuming that the initial angular velocity of the
flywheel is 240 rpm counterclockwise.
PROBLEM 17.9
The 10-in.-radius brake drum is attached to a
larger flywheel which is not shown. The total mass moment of
inertia of the flywheel and drum is 16 lb
ft
s
2
and the coefficient of
kinetic friction between the drum and the brake shoe is 0.40.
Knowing that the initial angular velocity is 240 rpm clockwise,
determine the force which must be exerted by the hydraulic cylinder
if the system is to stop in 75 revolutions.
1122
5053 392.7 0F
12.868 lbF
: 12.868 (0.40)
k
FN N
32.17 lbN
A
109.37 lb
B
PROBLEM 17.11
Each of the gears A and B has a mass of 2.4 kg and a radius of
gyration of 60 mm, while gear C has a mass of 12 kg and a radius
of gyration of 150 mm. A couple M of constant magnitude 10 N m
is applied to gear C. Determine (a) the number of revolutions of
gear C required for its angular velocity to increase from 100 to
450 rpm, (b) the corresponding tangential force acting on gear A.
3
25
250 rpm rad/s
3
AB
Gear A:
1
( ) (8.64 10 ) 2.9609 J
23
A
T
2
3
125
Gear C:
1
( ) (270 10 ) 14.8044 J
23
C
T
System: 11 1 1
() () () 20.726J
ABC
TT T T
37.5 rad/s
AB
PROBLEM 17.11 (Continued)
Gear A: 32
2
1
( ) (8.64 10 )(37.5 ) 59.957 J
A
T
1
39.898 radians
0.08
A
PROBLEM 17.12
Solve Problem 17.11, assuming that the 10-N m couple is applied
to gear B.
PROBLEM 17.11 Each of the gears A and B has a mass of 2.4 kg and
a radius of gyration of 60 mm, while gear C has a mass of 12 kg
and a radius of gyration of 150 mm. A couple M of constant
magnitude 10 N m is applied to gear C. Determine (a) the number
of revolutions of gear C required for its angular velocity to increase
from 100 to 450 rpm, (b) the corresponding tangential force acting
on gear A.
SOLUTION
Moments of inertia.
PROBLEM 17.12 (Continued)
0.08
A
PROBLEM 17.13
The gear train shown consists of four gears of the same
thickness and of the same material; two gears are of radius r,
and the other two are of radius nr. The system is at rest when
the couple
M
0
is applied to shaft C. Denoting by I
0
the moment
of inertia of a gear of radius r, determine the angular velocity of
shaft A if the couple
M
0
is applied for one revolution of shaft C.
2
1
0
A
n
In
2
0
1
I
n
PROBLEM 17.14
The double pulley shown has a mass of 15 kg and a
centroidal radius of gyration of 160 mm. Cylinder A
and block B are attached to cords that are wrapped on
the pulleys as shown. The coefficient of kinetic
friction between block B and the surface is 0.2.
Knowing that the system is at rest in the position
shown when a constant force P 200 N is applied to
cylinder A, determine (a) the velocity of cylinder A as
it strikes the ground, (b) the total distance that block
B moves before coming to rest.
SOLUTION
PROBLEM 17.14 (Continued)
and 0.150 m (1 m ) 0.6 m
0.250 m
B
BA
A
r
ss
r
To find F
f
use the free body diagram of block B.
0.250 m
0.250 m
BA
A
C
A
r
r
After the cylinder strikes the ground use the principle of work and energy applied to a system
consisting of block B and double pulley C.
132.305 J
When the system comes to rest,
4
0T
2
34
(25.487 N) (15 kg)(9.81 m/s )( sin 30 )
BB
Us s
BB
