Expanding the cross products and equation coefficients, we obtain the following two scalar equations
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Dynamics 2e 1251
Problem 6.76
A spool with inner radius
RD1:5
m rolls without slip over a
horizontal rail as shown. If the cable on the spool is unwound at a
rate
vAD5m=s
, in such a way that the unwound cable remains
perpendicular to the rail, determine the angular velocity of the
spool and the velocity of the spool’s center O.
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permission of McGraw-Hill, is prohibited.
Problem 6.77
A person is closing a heavy gate with rusty hinges by pushing the
gate with car
A
. If
wD24
m and
vAD1:2 m=s
, determine the
angular velocity of the gate when D15ı.
Solution
From the geometry of the problem, we can write the
y
position of
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1253
Problem 6.78
In the four-bar linkage system shown, let the circular guide with
center at
O
be fixed and such that, when
D0ı
, the bars
AB
and
BC
are vertical and horizontal, respectively. In addition, let
RD2ft, LD3ft, and HD3:5 ft.
When
D0ı
, the collar at
C
is sliding downward with a
speed of
23 ft=s
. Determine the angular velocities of the bars
AB
and BC at this instant.
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permission of McGraw-Hill, is prohibited.
Problem 6.79
In the four-bar linkage system shown, let the circular guide with
center at
O
be fixed and such that, when
D0ı
, the bars
AB
and
BC
are vertical and horizontal, respectively. In addition, let
RD2ft, LD3ft, and HD3:5 ft.
When
D37ı
,
ˇD25:07ı
,
D78:71ı
, and the collar
is sliding clockwise with a speed
vCD23 ft=s
. Determine the
angular velocities of the bars AB and BC .
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1255
Problem 6.80
In the four-bar linkage system shown, let the circular guide with
center at
O
be fixed and such that, when
D0ı
, the bars
AB
and
BC
are vertical and horizontal, respectively. In addition, let
RD2ft, LD3ft, and HD3:5 ft.
Determine the general expression for the angular velocities of
bars AB and BC as a function of ,ˇ,,R,L,H, and P
.
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permission of McGraw-Hill, is prohibited.
Problem 6.81
At the instant shown, the arm
OC
rotates counterclockwise with
an angular velocity of
35 rpm
about the fixed sun gear
S
of radius
RSD3:5 in:
The planet gear
P
with radius
RPD1:2 in:
rolls
without slip over both the fixed sun gear and the outer ring gear.
Finally, notice that the ring gear is not fixed, and it rolls without slip
over the sun gear. Determine the angular velocity of the ring gear and
the velocity of the center of the ring gear at the instant shown.
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permission of McGraw-Hill, is prohibited.
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Problem 6.82
The crank
AB
is rotating counterclockwise at a constant angular velocity
of
12 rad=s
while the pin
B
slides within the slot in the bar
CD
, which is
pinned at
C
. Letting
RD0:5
m,
hD1
m, and
dD0:25
m, determine
the angular velocity of
CD
at the instant shown (with points
A
,
B
, and
C
vertically aligned), as well as the velocity of the horizontal bar to which
bar CD is connected.
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Dynamics 2e 1259
Problem 6.83
For the slider-crank mechanism shown, let
RD20 mm
,
LD80 mm
, and
HD38 mm.
If
P
D1700 rpm
, determine the angular velocity of the connecting rod
AB and the speed of the slider Bfor D90ı.
0D RP
!AB pL2H2)!AB DRP
pL2H2D50:57 rad=s
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