PROBLEM 17.15
Gear A has a mass of 1 kg and a radius of gyration of 30 mm; gear B has a
mass of 4 kg and a radius of gyration of 75 mm; gear C has a mass of 9 kg
and a radius of gyration of 100 mm. The system is at rest when a couple
M0 of constant magnitude 4 N · m is applied to gear C. Assuming that no
slipping occurs between the gears, determine the number of revolutions
required for disk A to reach an angular velocity of 300 rpm.
32 3 2 3 2
322
222
1[0.9 10 (22.5 10 )(0.5 ) (90 10 )(0.16667 ) ]
2
(4.5125 10 kg m )
AA A
A
T
PROBLEM 17.15 (Continued)
Use the principle of work and energy applied to the system of all three gears with position 1 being the initial
rest position and position 2 being when 300 rpm.
A
2rad1min rev
300 31.416 rad/s
rev 60 s min
A
2rad/rev
PROBLEM 17.16
A slender rod of length l and weight W is pivoted at one end as shown. It is
released from rest in a horizontal position and swings freely. (a) Determine
the angular velocity of the rod as it passes through a vertical position
and determine the corresponding reaction at the pivot, (b) Solve part a for
W 1.8 lb and l 3 ft.
2
2W
PROBLEM 17.16 (Continued)
PROBLEM 17.17
A slender rod of length l is pivoted about a Point C located at a distance b
from its center G. It is released from rest in a horizontal position and swings
freely. Determine (a) the distance b for which the angular velocity of the rod
as it passes through a vertical position is maximum, (b) the corresponding
values of its angular velocity and of the reaction at C.
2
l
2
l
PROBLEM 17.17 (Continued)
Reaction at C.
2
ab
xt
xt
PROBLEM 17.18
A slender 9 lb rod can rotate in a vertical plane about a pivot at B. A spring
of constant k 30 lb/ft and of unstretched length 6 in. is attached to the rod
as shown. Knowing that the rod is released from rest in the position shown,
determine its angular velocity after it has rotated through 90°.
2
22
2
11
(30 lb/ft)(0.25 ft) 0.9375 lb ft
22
e
Vkx
PROBLEM 17.18 (Continued)
PROBLEM 17.19
An adapted golf device attaches to a wheelchair to help people
with mobility impairments play putt-putt. The stationary frame
OD is attached to the wheelchair, and a club holder OB is
attached to the pin at O. Holder OB is 6 in. long and weighs 8 oz,
and the distance between O and D is x= 1 ft. The putter shaft has
a length L= 36 in. and weighs 10 oz, while the putter head at A
weighs 12 oz. Knowing that the 1- lb/in. spring between D and B
is unstretched when = 90° and that the putter is released from
rest at = 0°, determine the putter head speed when it hits the
golf ball.
PROBLEM 17.19 (Continued)
,2 2AOA
A
PROBLEM 17.20
A 160-lb gymnast is executing a series of full-circle swings on
the horizontal bar. In the position shown he has a small and
negligible clockwise angular velocity and will maintain his
body straight and rigid as he swings downward. Assuming that
during the swing the centroidal radius of gyration of his body is
1.5 ft, determine his angular velocity and the force exerted on
his hands after he has rotated through (a) 90°, (b) 180°.
SOLUTION
Position 1. (Directly above the bar).
PROBLEM 17.20 (Continued)
y
PROBLEM 17.21
A collar with a mass of 1 kg is rigidly attached at a distance
d 300 mm from the end of a uniform slender rod AB. The rod has
a mass of 3 kg and is of length L 600 mm. Knowing that the rod
is released from rest in the position shown, determine the angular
velocity of the rod after it has rotated through 90°.
SOLUTION
PROBLEM 17.22
A collar with a mass of 1 kg is rigidly attached to a slender rod AB
of mass 3 kg and length L 600 mm. The rod is released from rest
in the position shown. Determine the distance d for which the
angular velocity of the rod is maximum after it has rotated 90°.
SOLUTION
Kinematics.
L
2
2
23
333
Lx
gx
PROBLEM 17.22 (Continued)
2/3Lg
is maximum. Set its derivative with respect to x equal to zero.
22
(3 3)(2) (2 3)(6 ) 0
dL x x x
PROBLEM 17.23
Two identical slender rods AB and BC are welded together to form
an L-shaped assembly. The assembly is pressed against a spring at
D and released from the position shown. Knowing that the
maximum angle of rotation of the assembly in its subsequent
motion is 90° counterclockwise, determine the magnitude of the
angular velocity of the assembly as it passes through the position
where rod AB forms an angle of 30° with the horizontal.
0.4
l
2
PROBLEM 17.24
The 30-kg turbine disk has a centroidal radius of gyration of 175 mm and
is rotating clockwise at a constant rate of 60 rpm when a small blade of
weight 0.5 N at Point A becomes loose and is thrown off. Neglecting
friction, determine the change in the angular velocity of the turbine disk
after it has rotated through (a) 90°, (b) 270°.
AAA
PROBLEM 17.24 (Continued)
Conservation of energy. 11 2 2
:TV T V
(b) Position 3. 270
Kinetic energy: 2
1
TI
mr
PROBLEM 17.25
A rope is wrapped around a cylinder of radius r and mass m as shown. Knowing that
the cylinder is released from rest, determine the velocity of the center of the cylinder
after it has moved downward a distance s.
3
3
PROBLEM 17.26
Solve Problem 17.25, assuming that the cylinder is replaced by a thin-walled pipe of
radius r and mass m.
PROBLEM 17.25
A rope is wrapped around a cylinder of radius r and mass m as
shown. Knowing that the cylinder is released from rest, determine the velocity of the
center of the cylinder after it has moved downward a distance s.