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Problem 6.142
Bar
AB
is pinned to the fixed support at
A
, and the pin
P
is fixed
to the disk at radius
Ri
. The disk with outer radius
Ro
rolls without
slipping over the horizontal flat surface with angular speed
!d
and
angular acceleration
˛d
in the directions shown. At the instant shown,
sD35 in:,RiD8:3 in:,RoD11 in:, and !dD15 rad=s.
If
˛d
is zero at the instant shown, determine the angular velocity
and angular acceleration of the bar AB.
sqs2.RoCRi/2D Psand .RoCRi/2!d
sDs!AB ;
s2and !AB D.RoCRi/2!d
s2
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.
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 6.143
Bar
AB
is pinned to the fixed support at
A
, and the pin
P
is fixed
to the disk at radius
Ri
. The disk with outer radius
Ro
rolls without
slipping over the horizontal flat surface with angular speed
!d
and
angular acceleration
˛d
in the directions shown. At the instant shown,
sD35 in:,RiD8:3 in:,RoD11 in:, and !dD15 rad=s.
If
˛dD30 rad=s2
at the instant shown, determine the angular
velocity and angular acceleration of the bar AB.
sqs2.RoCRi/2D Psand .RoCRi/2!d
sDs!AB ;
the solution of which is
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.
Dynamics 2e 1353
s22
Noting that
O
IDcos O{sin O|
and
O
JDsin O{Ccos O|
, this vector equation is equivalent to the following
two scalar equations in the unknowns ˛AB and Rs:
d
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 6.144
A vertical shaft has a base
B
that is stationary relative to an inertial
reference frame with vertical axis
Z
. Arm
OA
is attached to the
vertical shaft and rotates about the
Z
axis with an angular velocity
!OA D5rad=s
and an angular acceleration
˛OA D1:5 rad=s2
. The
´
axis is coincident with the
Z
axis, but is part of a reference frame
that rotates with the arm
OA
. The
x
axis of the rotating reference
frame coincides with the axis of the arm
OA
. At the instant shown,
the
y
axis is perpendicular to the page and directed into the page. At
this instant, the collar
C
is sliding along
OA
with a constant speed
vCD5ft=s
and is at a distance
dD1:2 ft
from the
´
axis. Compute
the inertial acceleration of the collar, and express it relative to the
rotating coordinate system.
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.
Dynamics 2e 1355
Problem 6.145
Let frames
A
and
B
be the frames with origins at points
A
and
B
, respectively. Point
B
does not move
relative to point A. The velocity and acceleration of point Prelative to frame Bare
EvPrel D.6:14 O{BC23:7 O|B/ft=s and EaPrel D.3:97 O{BC4:79 O|B/ft=s2:
Knowing that, at the instant shown, frame
B
rotates relative to frame
A
at a constant angular velocity
!BD1:2 rad=s
, that the position of point
P
relative to frame
B
is
ErP =B D.8 O{BC4:5 O|B/ft
, and that
frame
A
is fixed, determine the velocity and acceleration of
P
at the instant shown and express the results
using the frame Acomponent system.
Solution
Relating the velocity of Pto that of Bvia the rotating xByB´Breference frame, we obtain
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.
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.
Dynamics 2e 1357
Problem 6.146
Repeat Prob. 6.145, but express the results using the component
system of frame B.
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 6.147
A vertical shaft has a base
B
that is stationary relative to an inertial
reference frame with vertical axis
Z
. Arm
OA
is attached to the
vertical shaft and rotates about the
Z
axis with an angular velocity
!OA D5rad=s
and an angular acceleration
˛OA D1:5 rad=s2
. The
´
axis is coincident with the
Z
axis but is part of a reference frame
that rotates with the arm
OA
. The
x
axis of the rotating reference
frame coincides with the axis of the arm
OA
. At the instant shown,
the
y
axis is perpendicular to the page and directed into the page.
At this instant, the collar
C
is sliding along
OA
with a constant
speed
vCD3:32 m=s
and is rotating with a constant angular velocity
!CD2:3 rad=s
relative to the arm
OA
. At the instant shown, point
D
happens to be in the
x´
plane and is at a distance
`D0:05
m from
the
x
axis and at a distance
dD0:75
m from the
´
axis. Compute the
inertial acceleration of point
D
, and express it relative to the rotating
reference frame.
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.
Dynamics 2e 1359
Problem 6.148
Bar
AB
rotates about point
A
with angular speed
!1
and angular
acceleration
˛1
, both in the directions shown. The curved bar
BC
is pinned to bar
AB
at
B
and rotates with angular speed
!2
and
angular acceleration
˛2
about the pin at
B
in the directions shown,
relative to bar
AB
. At this instant, collar
D
is at the top of the
curved bar
BC
. The speed and acceleration of
D
relative to bar
BC
are given by
v0
and
a0
, respectively. Express your answers in
the
xy´
frame that is attached to bar
BC
with its origin at
B
.Hint:
As we will see in Eq. (10.14),
E!BC D E!AB C E!BC =AB D E!1C E!2
.
Determine the velocity of the collar
D
in terms of
d
,
!1
,
!2
,
R, and v0.
Solution
Using the given rotating reference frame, we can determine the velocity of Dusing
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.
