Problem 6.134
Using polar coordinates, obtain the acceleration of point
P
of the the mini-
example on p. 497; that is, obtain Eq. (6.56).
Solution
The polar coordinate system shown in the figure on the right rotates with the
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Dynamics 2e 1341
Problem 6.135
The disk
D
is rotating with angular speed
!D
about its central point
O
in the
direction shown. The particle
P
moves in the slot with known motion
s.t/
,
which is measured relative to the disk. Express your answers using the
xy´
frame that is attached to the disk Dwith its origin at Oas shown.
Determine the velocity of
P
as a function of
d
,
s
and its time derivatives,
and !D.
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permission of McGraw-Hill, is prohibited.
Problem 6.136
The disk
D
is rotating with angular speed
!D
about its central point
O
in the
direction shown. The particle
P
moves in the slot with known motion
s.t/
,
which is measured relative to the disk. Express your answers using the
xy´
frame that is attached to the disk Dwith its origin at Oas shown.
If
!D
is constant, determine the Coriolis acceleration of
P
and its total
acceleration as functions of d,sand its time derivatives, and !D.
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1343
Problem 6.137
The disk
D
is rotating with angular speed
!D
about its central point
O
in the
direction shown. The particle
P
moves in the slot with known motion
s.t/
,
which is measured relative to the disk. Express your answers using the
xy´
frame that is attached to the disk Dwith its origin at Oas shown.
If
!D
is increasing at the rate
P!D
, determine the Coriolis acceleration of
P
and its total acceleration as functions of
d
,
s
and its time derivatives,
!D
,
and P!D.
Solution
Using the given rotating frame, we write the acceleration of Pas
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permission of McGraw-Hill, is prohibited.
Problem 6.138
Bar
AB
rotates about point
A
with constant angular speed
!1
. Bar
BC
is pinned to bar
AB
at
B
and rotates with constant angular speed
!2
relative to bar
AB
about the pin at
B
. The position of collar
D
relative to bar
BC
is given by the coordinate
s
, which is a known
function of time. 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
, and
the position coordinate sand its time derivatives.
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1345
Problem 6.139
Bar
AB
rotates about point
A
with constant angular speed
!1
. Bar
BC
is pinned to bar
AB
at
B
and rotates with constant angular speed
!2
relative to bar
AB
about the pin at
B
. The position of collar
D
relative to bar
BC
is given by the coordinate
s
, which is a known
function of time. 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 acceleration of the collar
D
in terms of
d
,
!1
,
!2
,
and the position coordinate sand its time derivatives.
Solution
Using the given rotating frame, we write the acceleration of Das
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permission of McGraw-Hill, is prohibited.
Problem 6.140
Bar
AB
is pinned to the fixed support at
A
, and the collar
B
is pinned to the
bar at its opposite end. The bar
CD
can slide freely through the collar at
B
.
At the instant shown, bar
AB
is horizontal,
`D1:2
m,
sD1:07
m,
D60ı
,
and !AB D40 rad=s.
If
˛AB
is zero at the instant shown, determine the angular velocity and
angular acceleration of the bar CD.
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 6.141
Bar
AB
is pinned to the fixed support at
A
, and the collar
B
is pinned to the
bar at its opposite end. The bar
CD
can slide freely through the collar at
B
.
At the instant shown, bar
AB
is horizontal,
`D1:2
m,
sD1:07
m,
D60ı
,
and !AB D40 rad=s.
If
˛AB D15 rad=s2
at the instant shown, determine the angular velocity
and angular acceleration of the bar CD.
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.