Problem 6.105
A bar of length
LD2:5
m is falling so that, when
D34ı
,
vAD3m=s
and
aAD8:7 m=s2
. At this instant, determine the angular acceleration of the bar
AB and the acceleration of point D, where Dis the midpoint of the bar.
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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 6.106
A bar of length
LD8ft
and midpoint
D
is falling so that, when
D27ı
,
jEvDj D 18 ft=s
, and the vertical acceleration of point
D
is
23 ft=s2
downward.
At this instant, compute the angular acceleration of the bar and the acceleration
of point B.
2.sin O{cos O|/; (3)
which is equivalent to the following two scalar equations
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Dynamics 2e 1293
Now relating the acceleration of Dto that of A, we obtain
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Problem 6.107
Assuming that, for
0ı90ı
,
vA
is constant, compute the expression for
the acceleration of point D, the midpoint of the bar, as a function of and vA.
Solution
Referring to the figure on the right, we define a Cartesian coordinate system
with origin at
O
and axes
x
and
y
coinciding with the paths of points
A
and
B. Then, the position of point Dis given by
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Dynamics 2e 1295
Problem 6.108
The wheel
W
of radius
R
is rolling without slip with angular speed
!W
and angular acceleration
˛W
. The bar
AB
has length
3R
and is pinned
to the outer edge of the wheel at
A
; the end
B
remains in contact with
the surface. At the instant shown, determine the acceleration of point
B
.
Express your answer in the component system shown.
Solution
We start by determining the angular velocity of bar
AB
since it will be
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permission of McGraw-Hill, is prohibited.
Problem 6.109
At the instant shown, point
B
is moving with speed
vB
and acceleration
aB
. The bar
AB
has length
3R
; it is pinned to the outer edge of the
wheel at
A
, and the end
B
remains in contact with the surface. If the
wheel rolls without slip, determine the angular velocity
E!W
and angular
acceleration
E˛W
of the wheel at the instant shown. Express all your
answers in the component system shown.
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permission of McGraw-Hill, is prohibited.
2R D !2
2R D v2
4p5R2aB
2R
B
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permission of McGraw-Hill, is prohibited.
Problem 6.110
The wheel
W
of radius
R
is rolling without slip with angular speed
!W
and angular acceleration
˛W
. The bar
AB
has length
3R
and is pinned to
the outer edge of the wheel at
A
, and the end
B
remains in contact with
the surface. At the instant shown, determine the acceleration of point
B
.
Express your answer in the component system shown.
2p2and vBDR!WCR!AB DR!W11
2p2:
We know that the acceleration of
O
is given by
EaODR˛WO{
and so relating the acceleration of
A
to that of
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Dynamics 2e 1299
Problem 6.111
At the instant shown, point
B
is moving with speed
vB
and acceleration
aB
. The bar
AB
has length
3R
and is pinned to the outer edge of the wheel
at
A
, and the end
B
remains in contact with the surface. If the wheel rolls
without slip, determine the angular velocity
E!W
and angular acceleration
E˛W
of the wheel at the instant shown. Express all your answers in the
component system shown.
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permission of McGraw-Hill, is prohibited.