18 solution q. E. D

18–7.
SOLUTION
Ans.
=
283 ft
#
lb
T
=
1
2
a
50
32.2
(0.6)
2
b
(20)
2
+
1
2
a
20
32.2
b
C
(20)(1)
D
2
+
1
2
a
30
32.2
b
C
(20)(0.5)
D
2
T
=
1
2
I
O
v
2
O
+
1
2
m
A
v
2
A
+
1
2
m
B
v
2
B
1 ft
0.5ft
O
A
30 lb
B
20 lb
v
20 rad
/
s
The double pulley consists of two parts that are attached to
one another. It has a weight of 50 lb and a radius of gyration
about its center of 
k 
= 
0.6 ft and is turning with an angular
velocity of 20 rad
>
s clockwise. Determine the kinetic energy
of the system. Assume that neither cable slips on the pulley.
O
Ans:
T
=
283 ft
#
lb

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919
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*18–8.
1 ft
0.5 ft
O
A
30 lb
B
20 lb
v
20 rad
/
s
The double pulley consists of two parts that are attached to
one another. It has a weight of 50 lb and a centroidal radius
of gyration of 
and is turning with an angular
velocity of 20 rad s clockwise. Determine the angular
velocity of the pulley at the instant the 20-lb weight moves
2 ft downward.
>
k
O
=
0.6 ft
SOLUTION