Problem 6.61
As the circular cam, whose center is at
A
rotates, it causes the follower
B
to move back and forth. The cam angle is
, the radius of the cam
is
R
, and the angular speed of the cam is
P
D!OA
. The cam is
pin-connected to the fixed point O.
Using the given
x
coordinate, determine the velocity of the fol-
lower at the instant
D30ı
if
RD1:5 in:
, and
P
D!OA D
1000 rpm.
Differentiating Eq. (1) with respect to time, we obtain
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Dynamics 2e 1231
Problem 6.62
As the circular cam, whose center is at
A
rotates, it causes the follower
B
to move back and forth. The cam angle is
, the radius of the cam
is
R
, and the angular speed of the cam is
P
D!OA
. The cam is
pin-connected to the fixed point O.
Using the given
x
coordinate, determine the velocity of the fol-
lower as a function of the cam angle
, the radius of the cam
R
, and
the given angular speed of the cam !OA.
Differentiating Eq. (1) with respect to time, we obtain
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Problem 6.63
At the instant shown, the lower rack is moving to the right with a speed
of
2:7 m=s
while the upper rack is moving to the left with a speed
of
1:7 m=s
. If the nominal radius of the pinion
O
is
RD0:25
m,
determine the angular velocity of the pinion, as well as the position of
the pinion’s instantaneous center of rotation relative to point O.
2R )!PD8:800 rad=s) E!PD8:800 O
where we have used
vLD2:7 m=s
,
vUD 1:7 m=s
, and
RD0:25
m. To find the position of the IC, we
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Dynamics 2e 1233
Problem 6.64
A carrier is maneuvering so that, at the instant shown,
jEvAj D
22 kn
,
D35ı
,
jEvBj D 24 kn
(1 kn is equal to 1 nautical mile
(nml) per hour or
6076 ft=h
). Letting
D19ı
and the distance
between
A
and
B
be
720 ft
, determine the ship’s turning rate at
the given instant if the ship is rotating clockwise.
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permission of McGraw-Hill, is prohibited.
Problem 6.65
For the slider-crank mechanism shown, let
RD1:9 in:
,
LD6:1 in:
, and
HD1:2 in:
Also, at the instant shown, let
D27ı
and
!AB D4850 rpm
.
Determine the velocity of the piston at the instant shown.
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Dynamics 2e 1235
Using this expression for tan , Eq. (5) becomes
6
R
Lsin
7
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permission of McGraw-Hill, is prohibited.
Problem 6.66
For the slider-crank mechanism shown, let
RD1:9 in:
,
LD6:1 in:
, and
HD1:2 in:
Also, at the instant shown, let
D27ı
and
!AB D4850 rpm
.
Determine P
and the velocity of point Dat the instant shown.
0D R!AB sin L!BC cos ; (3)
vCDR!AB cos L!BC sin : (4)
The first equation can be solved for !BC to obtain
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Dynamics 2e 1237
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permission of McGraw-Hill, is prohibited.
Problem 6.67
A wheel
W
of radius
RWD7mm
is connected to point
O
via the rotating
arm OC, and it rolls without slip over the stationary cylinder
S
of radius
RSD15 mm
. If, at the instant shown,
D63ı
and
!WD9rad=s
,
determine the angular velocity of the arm
OC
and the velocity of point
P
,
where point
P
lies on the edge of
W
and is vertically aligned with point
C
.
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1239
Problem 6.68
At the instant shown, the center
O
of a spool with inner and outer
radii
rD1
m and
RD2:2
m, respectively, is moving up the incline at
speed
vOD3m=s
. If the spool does not slip relative to the ground or
relative to the cable
C
, determine the rate at which the cable is wound
or unwound, that is, the length of cable being wound or unwound per
unit time.
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permission of McGraw-Hill, is prohibited.