15.30
A pulley and two loads are connected by inextensible cords
as
shown. Load
A
has a constant acceleration
of
300 mm/s
2
and an
initial velocity
of
240 mm/s,
both
directed upward.
Determine
(a)
the number
of
revolutions executed by
the
pulley in 3 s,
(b)
the
velocity and position
of
load
B
after 3 s, (
c)
the acceleration
of
point
D
on
the
rim
of
the
pulley at
t
=
0.
15.31
A pulley and two loads are connected by inextensible cords
as
shown. The pulley starts from rest at
t
=
0 and
is
accelerated at
the uniform rate
of
2.4 rad/s
2
clockwise.
At
t
=
4 s, determine
the
velocity and position
(a)
of
load
A,
(b)
of
load
B.
15.32
Disk
B
is
at rest when it
is
brought into contact with disk
A
which
is
rotating freely at 450 rpm clockwise. After 6 s
of
slippage, during
which each disk has a constant angular acceleration, disk
A
reaches
a final angular velocity
of
140 rpm clockwise. Determine the angu
lar acceleration
of
each disk during
the
period
of
slippage.
Fig. P15.32
and
P15.33
15.33
and
15.34
A simple friction drive consists
of
two disks
A
and
B.
Initially, disk
A
has a clockwise angular
ve
locity
of
500
rpm
and
disk
B
is
at rest.
It
is
known that disk
A
will coast to rest in 60 s.
However, rather than waiting until both disks
ar
e at rest to bring
them together, disk
B
is
given a constant angular acceleration
of
2.5 rad/s
2
counterclockwise. Determine
(a)
at what time
the
disks
can be brought together
if
they are not to slip,
(b)
the angular veloc
ity
of
each disk as contact
is
made.
15.35
Two
friction disks
A
and
B
are both rotating freely at 240 rpm
counterclockwise when they are brought into contact. After 8 s
of
slippage, during which each disk has a constant angular accelera
tion, disk
A
reaches a final angular velocity
of
60 rpm counter
clockwise. Determine
(
a)
the angular acceleration
of
each disk
during the period
of
slippage,
(b)
the
time at which the angular
D
Fig
. P15.30
and
P15.31
velocity
of
disk
B
is
equal to zero.
Fig.
P15.34
and
P15.35
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15.48
In the planetary gear system shown, the radius of gears
A,
B,
C,
and
D
is
3
in.
and the radius of the outer gear
E
is
9
in.
Knowing that
gear
E
has an angular velocity of 120 rpm clockwise and that the
central gear has an angular velocity of 150 rpm clockwise, determine
(a)
the angular velocity of each planetary gear,
(b)
the angular veloc
ity of the spider connecting the planetary gears.
Fig. P15.48
and
P15.49
15.49
In the planetary gear system shown the radius
of
the central gear
A
is
a,
the radius of each
of
the planetary gears
is
b,
and the
radius
of
the outer gear
E
is
a
+
2b.
The angular velocity
of
gear
A
is
wA
clockwise, and
the
outer gear
is
stationary.
If
the angular
velocity
of
the spider
BCD
is
to be
wA/5
clockwise, determine
(a)
the
required value of the ratio
b!a
,
(b)
the
corresponding angu
lar velocity of each planetary gear.
15.50
Gear
A
rotates with an angular velocity
of
120 rpm clockwise.
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 Spring '08
 murakami
 Acceleration, Angular velocity, Velocity

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