where we have used the fact that PxDvCand P
D!C.
To find the acceleration of D, we can relate the acceleration of Dto that of Ousing
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Dynamics 2e 1411
Problem 6.175
Let frames
A
and
B
have their 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 A, which is fixed, are
EvPD.14:9 O{AC19:4 O|A/ft=s and EaPD.1:78 O{AC5:96 O|A/ft=s2:
Knowing that frame
B
rotates relative to frame
A
at a constant angular velocity
!BD1:2 rad=s
and
that the position of point
P
relative to frame
B
is
ErP =B D.8 O{BC4:5 O|B/ft
, determine the velocity
and acceleration of
P
relative to frame
B
at the instant shown. Express the results using the frame
A
component 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.
where it is given that EaBDE
0, that
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1413
Problem 6.176
The wheel
D
rotates without slip over a curved cylindrical
surface with constant radius of curvature
LD1:6 ft
and
center at the fixed point
E
. The
XY
frame is attached
to the rolling surface, and it is inertial. The
xy
frame is
attached to
D
at
O
and rotates with it at a constant angular
velocity
!DD14 rad=s
. Collar
C
slides along the bar
AB
with a constant velocity
vCD4ft=s
relative to the
xy
frame. At the instant shown, points
O
and
E
are vertically
aligned. Letting
`D0:25 ft
and
RD1ft
, determine the
inertial velocity and acceleration of
C
at the instant shown
when
D25ı
and the
xy
frame is parallel to the
XY
frame. Express your result in the xy and XY frames.
where we have used
RD1ft
,
`D0:25 ft
,
!DD14 rad=s
,
vCD4ft=s
, and
D25ı
to obtain the numerical
result, and we have used the fact that, at this instant, O{DO
I,O|DO
J, and O
kDO
K.
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 1415
Problem 6.177
The wheel
D
rotates without slip over a curved cylindri-
cal surface with constant radius of curvature
LD1:6 ft
and center at the fixed point
E
. The
XY
frame is at-
tached to the rolling surface, and it is inertial. The
xy
frame is attached to
D
at
O
and rotates with it at an an-
gular velocity
!DD14 rad=s
and an angular acceleration
˛DD1:3 rad=s2
. Collar
C
slides along the bar
AB
with
a constant velocity
vCD4ft=s
relative to the
xy
frame.
Letting
`D0:25 ft
and
RD1ft
, determine the inertial
velocity and acceleration of
C
, at the instant shown, when
D25ı
and the
xy
frame is parallel to the
XY
frame.
Express your result in the xy and XY frames.
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.