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PROBLEM 15.239 (Continued)
2
0.25 (2.5 3 )
(0.625 3 m/s )
BB
′′
= ×
= ×
= −
aΩv
ji
k
Motion of Point B relative to the frame.
PROBLEM 15.239 (Continued)
2 /boom
22
/ /boom
/ /boom 2 /boom
2 (2)(0.40 ) (1.5sin30 1.5cos30 )
(1.03923 ft/s ) (0.6 ft/s )
4 3 4 1.5sin30 1.5cos30
(6.1782 ft/s) (5.299 ft/s)
2
1.6 1.6 3 0 1.0392
B
BF B B
BF B B B
′′
′′
× = × °+ °
=−+
= +
=− + + °+ °
=−+
=+ +×
=− − +−
Ωv i j k
jk
v vv
jk j k
jk
a aa Ωv
jk
22
3 0.6
(2.6392 ft/s ) (2.1713 ft/s )
+
=−−
jk
jk
Velocity of Point B.
/
2.5 3 6.1782 5.299
B B BF
B
′
= +
=−+
vvv
v i jk
1/
1/
2
2 (2)(0.25 ) ( 6.1782 5.299 )
(2.6495 ft/s )
BF
× = ×− +
=
v j jk
i
Ω
PROBLEM 15.240
The vertical plate shown is welded to arm EFG, and the entire unit rotates at
the constant rate
1
1.6
ω
=
rad/s about the Y axis. At the same time, a
continuous link belt moves around the perimeter of the plate at a constant
speed
4.5 in./s.u=
For the position shown, determine the acceleration of the
link of the belt located (a) at Point A, (b) at Point B.
PROBLEM 15.240 (Continued)
(b) Acceleration of Point B.
22
/
(5 in.) (10 in.) (3 in.)
1.6 ( 5 10 3 )
(4.8 in./s) (8 in./s)
1.6 (4.8 8 )
(12.8 in./s ) (7.68 in./s )
B
BB
BB
BF
u
′
′′
=−+ +
= ×
= ×− + +
= +
= ×
=×+
= −
= −
r i jk
vr
j i jk
ik
av
j ik
ik
vj
Ω
Ω
PROBLEM 15.241
The vertical plate shown is welded to arm EFG, and the entire unit rotates at
the constant rate
1
1.6
ω
=
rad/s about the Y axis. At the same time, a
continuous link belt moves around the perimeter of the plate at a constant
speed
4.5 in./s.u=
For the position shown, determine the acceleration of
the link of the belt located (a) at Point C, (b) at Point D.
PROBLEM 15.241 (Continued)
(b) Acceleration at Point D.
22
/
(5 in.) (10 in.) (3 in.)
1.6 ( 5 10 3 )
(4.8 in./s) (8 in./s)
1.6 ( 4.8 8 )
(12.8 in./s ) (7.68 in./s )
(4.5 in./s)
D
DB
DB
DF
u
′
′′
=−+ −
= ×
= ×− + −
=−+
= ×
= ×− +
= +
= =
r i jk
vr
j i jk
ik
av
j ik
ik
vj j
Ω
Ω
PROBLEM 15.242
A disk of 180-mm radius rotates at the constant rate
ω
2
12=
rad/s with respect to arm CD, which itself rotates at
the constant rate
1
8
ω
=
rad/s about the Y axis. Determine at
the instant shown the velocity and acceleration of Point A on
the rim of the disk.
PROBLEM 15.242 (Continued)
Coriolis acceleration.
/
2
AF
×
Ωv
PROBLEM 15.243
A disk of 180-mm radius rotates at the constant rate
ω
2
12=
rad/s with respect to arm CD, which itself rotates at
the constant rate
1
8
ω
=
rad/s about the Y axis. Determine at
the instant shown the velocity and acceleration of Point B on
the rim of the disk.
PROBLEM 15.243 (Continued)
Coriolis acceleration.
/
2
BF
×vΩ
