Problem 6.16
The bent rod rotates about an axis connecting points Aand E. All bends
in the rod are
90ı
angles, and the given dimensions are
hD21 cm
,
`D14:5 cm
,
dD21 cm
, and
bD7:6 cm
. Express all your answers
using the component system shown.
If, at the instant shown, the rod is rotating with a constant angular
speed of
25 rad=s
and the rotation is counterclockwise as viewed from
A
looking toward E, determine the velocity and acceleration of point C.
jErA=E jDbO
jErA=E jDdO{C`O|C.b Ch/ O
Substituting Eq. (3), the first of Eqs. (4), and Eq. (5) into Eq. (1), we obtain
k
k
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Dynamics 2e 1171
For the acceleration of C, we substitute Eq. (3), the second of Eqs. (4), and Eq. (5) into Eq. (2) to obtain
k
k
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Problem 6.17
The bent rod rotates about an axis connecting points Aand E. All bends
in the rod are
90ı
angles, and the given dimensions are
hD21 cm
,
`D14:5 cm
,
dD21 cm
, and
bD7:6 cm
. Express all your answers
using the component system shown.
If, at the instant shown, the rod is rotating with an angular speed
of
20 rad=s
, it is decreasing at a rate of
14 rad=s2
, and the rotation is
clockwise as viewed from
A
looking toward
E
, determine the velocity
and acceleration of point B.
jErE=AjDhO
jErE=AjDdO{`O|.b Ch/ O
Substituting Eq. (3), the first of Eqs. (4), and Eq. (5) into Eq. (1), we obtain
dO{`O|.b Ch/ O
k
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1173
dO{`O|.b Ch/ O
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.
Problem 6.18
The bent rod rotates about an axis connecting points Aand E. All bends
in the rod are
90ı
angles, and the given dimensions are
hD21 cm
,
`D14:5 cm
,
dD21 cm
, and
bD7:6 cm
. Express all your answers
using the component system shown.
If, at the instant shown, the rod is rotating with an angular speed of
15 rad=s
, it is increasing at a rate of
8rad=s2
, and the rotation is clock-
wise as viewed from
A
looking toward
E
, determine the velocity and
acceleration of point C.
jErE=AjDhO
jErE=AjDdO{`O|.b Ch/ O
Substituting Eq. (3), the first of Eqs. (4), and Eq. (5) into Eq. (1), we obtain
dO{`O|.b Ch/ O
k
k
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1175
dO{`O|.b Ch/ O
k
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permission of McGraw-Hill, is prohibited.
Problem 6.19
The rectangular block is attached to a rod that runs through the
block along a diagonal. The rod is mounted in bearings at
A
and
B
that allow it to rotate about its own axis. The given dimensions are
hD8:5 cm
,
`D20 cm
, and
dD22 cm
. Express all your answers
using the component system shown.
If, at the instant shown, the rod is rotating with an angular speed
of
18 rad=s
, it is increasing at a rate of
3rad=s2
, and the rotation is
counterclockwise as viewed from
A
looking toward
B
, determine
the velocity and acceleration of point E.
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1177
For the acceleration of E, we substitute Eq. (3), the second of Eqs. (4), and Eq. (5) into Eq. (2) to obtain
dO{hO|C`O
k
k
k
bO
where we have used the fact that
EaODE
0
. Using
`D20 cm
,
dD22 cm
,
hD8:5 cm
,
!bD18 rad=s
, and
˛bD3rad=s2, the acceleration of Ebecomes
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permission of McGraw-Hill, is prohibited.
Problem 6.20
The rectangular block is attached to a rod that runs through the
block along a diagonal. The rod is mounted in bearings at
A
and
B
that allow it to rotate about its own axis. The given dimensions are
hD8:5 cm
,
`D20 cm
, and
dD22 cm
. Express all your answers
using the component system shown.
If, at the instant shown, the rod is rotating with an angular speed
of
35 rad=s
, it is decreasing at a rate of
5rad=s2
, and the rotation is
counterclockwise as viewed from
A
looking toward
B
, determine
the velocity and acceleration of point D.
jErQ=O jDhO|CdO{C`O
jErQ=O jDdO{hO|C`O
Substituting Eq. (3), the first of Eqs. (4), and Eq. (5) into Eq. (1), we obtain
dO{hO|C`O
k
k
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1179
For the acceleration of D, we substitute Eq. (3), the second of Eqs. (4), and Eq. (5) into Eq. (2) to obtain
dO{hO|C`O
k
k
k
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permission of McGraw-Hill, is prohibited.