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730
16–97.
SOLUTION
If the hub gear
H
and ring gear
R
have angular velocities
vH=5 rad>s and vR=20 rad>s, respectively, determine
the angular velocity vS of the spur gear S and the angular
velocity of its attached arm OA.
ω
S
ω
R
ω
O
150 mm
50 mm
A
S
H
250 mm
731
16–98.
SOLUTION
If the hub gear H has an angular velocity vH= 5 rad
>
s,
determine the angular velocity of the ring gear R so that
the arm OA attached to the spur gear S remains stationary
(vOA =0). What is the angular velocity of the spur gear?
H
ω
S
ω
R
ω
O
150 mm
50 mm
A
S
H
250 mm
732
16–99.
SOLUTION
The crankshaft AB rotates at about the
fixed axis through point A, and the disk at Cis held fixed in
its support at E. Determine the angular velocity of rod CD
at the instant shown.
vAB =50 rad
>
s
E
C
D
F
75 mm
40 mm 75 mm
300 mm
733
*16–100.
Cylinder A rolls on the fixed cylinder B without slipping. If
bar CD is rotating with an angular velocity of
v
CD
=
3 rad
>
s, determine the angular velocity of A.
SOLUTION
C
D
A
200 mm
vCD
734
16–101.
The planet gear A is pin connected to the end of the link
BC. If the link rotates about the fixed point B at
4 rad
>
s, determine the angular velocity of the ring gear R.
The sun gear D is fixed from rotating.
SOLUTION
R
D
BC
A
150 mm 75 mm
v
R
vBC 4 rad/s
735
16–102.
Solve Prob. 16–101 if the sun gear D is rotating clockwise
atvD
=5 rad>s
while link BC rotates counterclockwise at
vBC
=4 rad>s
.
R
D
BC
A
150 mm 75 mm
vR
vBC 4 rad/s
SOLUTION
736
16–103.
Bar AB has the angular motions shown. Determine the
velocity and acceleration of the slider block C at this instant.
1 m
0.5 m
B
A
45
vAB fi 4 rad/s
AB fi 6 rad/s2
a
737
*16–104.
At a given instant the bottom Aof the ladder has an
acceleration
and velocity both
acting
to the left. Determine the acceleration of the top of
the
ladder, B, and the ladder’s angular acceleration at this
same instant.
vA=6ft>s,aA=4ft>s2
B
16 ft
SOLUTION
738
16–105.
At a given instant the top Bof the ladder has an
acceleration and a velocity of both
acting downward. Determine the acceleration of the
bottom Aof the ladder, and the ladder’s angular
acceleration at this instant.
vB=4ft>s,aB=2ft>s2
SOLUTION
B
16 ft
739
16–106.
Member AB has the angular motions shown. Determine the
velocity and acceleration of the slider block C at this instant.
2 m
0.5 m
4 rad/s
5 rad/s2
A
C
B
5
3
SOLUTION
740
16–107.
At a given instant the roller A on the bar has the velocity
and acceleration shown. Determine the velocity and
acceleration of the roller B, and the bar’s angular velocity
and angular acceleration at this instant.
SOLUTION
A
0.6 m
30
30
4 m/s
6 m/s2
741
Ans:
v
B=8 ft>s
c
a
B=
21.4 ft
>
s
2
u=2.39°
*16–108.
SOLUTION
The rod is confined to move along the path due to the pins
at its ends. At the instant shown, point Ahas the motion
shown. Determine the velocity and acceleration of point B
at this instant.
3ft
5 ft
A
B
v
A
=6ft/s
a
A
=3ft/s
2
742
16–109.
Member AB has the angular motions shown. Determine the
angular velocity and angular acceleration of members CB
and DC.
vAB 2 rad/s
aAB 4 rad/s2
200 mm
450 mm
60fi
100 mm
B
A
D
C
SOLUTION
743
16–110.
The slider block has the motion shown. Determine the
angular velocity and angular acceleration of the wheel at
this instant.
SOLUTION
400 mm
A
C
B
150 mm
vB 4 m/s
744
16–111.
At a given instant the slider block A is moving to the right
with the motion shown. Determine the angular acceleration
of link AB and the acceleration of point B at this instant.
2 m
2 m
30A
B
vA fi
4 m
/
s
aA fi 6 m/s2
SOLUTION
745
*16–112.
Determine the angular acceleration of link CD if link AB
has the angular velocity and angular acceleration shown.
SOLUTION
0.5 m
0.5 m
1 m
C
D
aAB 6 rad/s2
746
*16–112. Continued
747
16–113.
The reel of rope has the angular motion shown. Determine
the velocity and acceleration of point A at the instant shown.
B
100 mm
C
3 rad/s
8 rad/s2
v
a
SOLUTION
748
16–114.
The reel of rope has the angular motion shown. Determine
the velocity and acceleration of point B at the instant shown.
SOLUTION
B
100 mm
C
3 rad/s
8 rad/s2
v
a
749
16–115.
G
B
r
2r
v
A
A cord is wrapped around the inner spool of the gear. If it is
pulled with a constant velocity v, determine the velocities
and accelerations of points Aand B.The gear rolls on the
fixed gear rack.
SOLUTION
Ans:
vB=4v S
v
A=
2
2
2v
u=45°
a
aB=
2
v
2
r
T
aA=
2v
2
r
S
