18 solution q. E. D

Ans.
500 mm
400 mm
250 mm
30
°
P
A
G
B
Ans:
v
=
2.02 rad
>
s

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917
© 2016 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently 
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 
18–6.
A force of 
P
=
20 N is applied to the cable, which causes 
the 175-kg reel to turn without slipping on the two rollers 
A
and 
B
of the dispenser. Determine the angular velocity of 
the reel after it has made two revolutions starting from rest. 
Neglect the mass of the cable. Each roller can be considered 
as an 18-kg cylinder, having a radius of 0.1 m. The radius of 
gyration of the reel about its center axis is 
k
G
=
0.42 m.
SOLUTION
System:
T
1
+
Σ
U
1
-
2
=
T
2
[0
+
0
+
0]
+
20(2)(2
p
)(0.250)
=
1
2
3
175(0.42)
2
4
v
2
+
2
c
1
2
(18)(0.1)
2
d
v
2
r
v
=
v
r
(0.1)
=
v
(0.5)
v
r
=
5
v
Solving:
v
=
1.78 rad
>
s 
Ans.
500 mm
400 mm
250 mm
30
°
P
A
G
B
Ans:
v
=
1.78 rad
>
s

---

918
© 2016 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently 
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.