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PROBLEM 15.181*
Rod AB passes through a collar that is welded to link DE. Knowing that
at the instant shown block A moves to the right at a constant speed of 75
in./s, determine (a) the angular velocity of rod AB, (b) the velocity
relative to the collar of the point of the rod in contact with the collar, (c)
the acceleration of the point of the rod in contact with the collar. (Hint:
Rod AB and link DE have the same
ω
and the same
.)α
PROBLEM 15.181* (Continued)
For rod AB,
3.6085 rad/s
AB
=ω
2
52.624 rad/s
AB
=α
c
6
PD
α
′
= =
aa
30 6
ω
°+
60°
2
[315.74 in./s
=
2
30 ] [78.13 in./s°+
60 ]
°
PROBLEM 15.182*
Solve Problem 15.181, assuming that block A moves to the left at a
constant speed of
75 in./s.
PROBLEM 15.181 Rod AB passes through a collar which is welded
to link DE. Knowing that at the instant shown block A moves to the
right at a constant speed of 75 in./s, determine (a) the angular
velocity of rod AB, (b) the velocity relative to the collar of the point
of the rod in contact with the collar, (c) the acceleration of the point
of the rod in contact with the collar. (Hint: Rod AB and link DE have
the same
ω
and the same
.)α
PROBLEM 15.182* (Continued)
For rod AB,
3.6085 rad/s
AB
=ω
2
52.624 rad/s
AB
=
α
PROBLEM 15.183*
In Problem 15.157, determine the acceleration of pin P.
PROBLEM 15.157 The motion of pin P is guided by slots cut in
rods AD and BE. Knowing that bar AD has a constant angular
velocity of 4 rad/s clockwise and bar BE has an angular velocity
of 5 rad/s counterclockwise and is slowing down at a rate of
2 rad/s2, determine the velocity of P for the position shown.
PROBLEM 15.183* (Continued)
PROBLEM 15.184
The bowling ball shown rolls without slipping on the horizontal xz plane with an
angular velocity
xyz
ωωω
=++i jk
ω
. Knowing that
(4.8 m/s) (4.8 m/s) (3.6 m/s)
A
=−+v ijk
and
(9.6 m/s)
D
=vi
(7.2 m/s) ,+k
determine (a) the angular velocity of the bowling ball, (b) the
velocity of its center C.
PROBLEM 15.185
The bowling ball shown rolls without slipping on the horizontal xz plane with an
angular velocity
xyz
ωωω
=++i jk
ω
. Knowing that
(3.6 m/s) (4.8 m/s) (4.8 m /s)
B
=−+v ijk
and
(7.2 m/s)
D
=vi
(9.6 m/s) ,+k
determine (a) the angular velocity of the bowling ball, (b) the
velocity of its center C.
PROBLEM 15.186
Plate ABD and rod OB are rigidly connected and rotate about
the ball-and-socket joint O with an angular velocity
ω
=
ω
x
i +
ω
x
j +
ω
z k. Knowing that vA = (80 mm/s)i + (360 mm/s)j +
(vA)z k and
1.5 rad/s,
x
ω
=
determine (a) the angular velocity
of the assembly, (b) the velocity of Point D.
PROBLEM 15.186 (Continued)
(b) Velocity of D.
1.5 3.5 3.0
160 120 80
(360 280) ( 480 120) (180 560)
DD
= ×
= −−
++−
= + +− + + +
vr
i jk
i jk
ω
