PROBLEM 15.227 (Continued)
(a) Velocity of Point D.
/
(0.75 m/s) (0.75 3 m/s) ( 3 m/s)
D D DF
D
′
= +
=+−
vvv
v i jk
PROBLEM 15.228
Manufactured items are spray–painted as
they pass through the automated work station
shown. Knowing that the bent pipe ACE
rotates at the constant rate
1
0.4 rad/s
ω
=
and
that at Point D the paint moves through the
150 mm/s,u=
determine, for the position
shown, (a) the velocity of the paint at D,
(b) the acceleration of the paint at D.
PROBLEM 15.229
Solve Problem 15.227, assuming that at the instant shown the angular
velocity
ω
1 of the plate is 10 rad/s and is decreasing at the rate of 25 rad/s2,
while the relative speed u of Point D of strap CD is 1.5 m/s and is decreasing
at the rate of 3 m/s2.
PROBLEM 15.227 The circular plate shown rotates about its vertical
diameter at the constant rate
110 rad/s.
ω
=
Knowing that in the position
shown the disk lies in the XY plane and Point D of strap CD moves upward at
a constant relative speed u
1.5 m/s,=
determine (a) the velocity of D, (b) the
acceleration of D.
PROBLEM 15.229 (Continued)
(a) Velocity of Point D.
/
(0.75 m/s) (0.75 3 m/s) ( 3 m/s)
D D DF
D
′
= +
=+−
vvv
v i jk
PROBLEM 15.230
Solve Prob. 15.225, assuming that at the instant shown the
angular velocity
1
ω
of the rod is 5 rad/s and is increasing at
the rate of 10
2
rad/s ,
while the relative speed u of the collar C
is 39 in./s and is decreasing at the rate of 260
2
in./s .
PROBLEM 15.231
Using the method of Section 15.7A, solve Problem 15.192.
PROBLEM 15.192 In the system shown, disk A is free to rotate about
the horizontal rod OA. Assuming that shaft OC and disk B rotate with
constant angular velocities
1
ω
and
2
,
ω
respectively, both
counterclockwise, determine (a) the angular velocity of A, (b) the
angular acceleration of disk A.
PROBLEM 15.231 (Continued)
Coefficient of j:
00
xx
R
ωω
= →=
PROBLEM 15.232
Using the method of Section 15.7A, solve Problem 15.196.
PROBLEM 15.196 A 3–in.–radius disk spins at the constant rate
ω
2
4=
rad/s about an axis held by a housing attached to a
horizontal rod that rotates at the constant rate
1
5
ω
=
rad/s.
Knowing that
30 ,
θ
= °
determine the acceleration of Point P on
the rim of the disk.
PROBLEM 15.233
Using the method of Section 15.7A, solve
Problem 15.198.
PROBLEM 15.198 At the instant shown, the
robotic arm ABC is being rotated simultaneously
at the constant rate
1
0.15
ω
=
rad/s about the y
axis, and at the constant rate
2
0.25
ω
=
rad/s
about the z axis. Knowing that the length of arm
ABC is 1 m, determine (a) the angular
acceleration of the arm, (b) the velocity of Point
C, (c) the acceleration of Point C.
PROBLEM 15.233 (Continued)
(b) Velocity of C.
/C C CF
′
= +
vvv