Problem 6.7
Letting
RAD203 mm
,
RBD107 mm
,
RCD165 mm
, and
RDD140 mm
, determine the angular
acceleration of gears
B
,
C
, and
D
when gear
A
has an angular acceleration with magnitude
j˛Aj D
47 rad=s2
in the direction shown. Note that gears
B
and
C
are mounted on the same shaft and they rotate
together as a unit.
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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 6.8
The bevel gears
A
and
B
have nominal radii
RAD20 mm
and
RBD5mm
,
respectively, and their axes of rotation are mutually perpendicular. If the angular
speed of gear Ais !AD150 rad=s, determine the angular speed of gear B.
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Dynamics 2e 1163
Problem 6.9
A rotor with a fixed spin axis through point
O
is accelerated from rest with a constant
angular acceleration
˛rD0:5 rad=s2
. If the rotor’s diameter is
dD15 ft
, determine the
time it takes for the point
P
on the outer edge of the rotor to reach a speed
vPD300 ft=s
and the magnitude of the acceleration of Pwhen the speed vPis achieved.
Photo credit: NASA
Solution
Points on the outer edge of the rotor have a speed
vD1
2djE!rj
, where
E!rD!rO
k
is the
angular velocity of the rotor. Letting
t300
be the time at which
vPD300 ft=s
is achieved,
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Problem 6.10
A Pelton turbine (a type of turbine used in hydroelectric power generation) is spinning at
1100 rpm
when
the water jets acting on it are shut off, thus causing the turbine to slow down. Assuming that the angular
deceleration rate is constant and equal to
1:31 rad=s2
, determine the time it takes for the turbine to stop. In
addition, determine the number of revolutions of the turbine during the spin-down.
Photo credit: Courtesy of Andritz Hydro, Austria
pt D !2
2˛pt D5065 rad )pt D806:1 rev:(4)
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Dynamics 2e 1165
Problem 6.11
The sprinkler shown consists of a pipe
AB
mounted on a hollow vertical shaft. The water comes in the
horizontal pipe at
O
and goes out the nozzles at
A
and
B
, causing the pipe to rotate. Letting
dD7in:
,
determine the angular velocity of the sprinkler
E!s
, and
jEaBj
, the magnitude of the acceleration of
B
, if
B
is moving with a constant speed vBD20 ft=s. Assume that the sprinkler does not roll on the ground.
dD34:29 rad=s) E!sD34:29 Ou´rad=s;(5)
where we have used
vBD20 ft=s
and
dD7in:D0:5833 ft
, along with the fact that the sprinkler is rotating
in the positive
Ou´
direction. Since
vB
is constant, the first of Eqs. (5) tells us that
!s
is also constant, and
therefore
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Problem 6.12
In a carnival ride, two gondolas spin in opposite directions about a fixed axis. If
`D4
m, determine the
maximum constant angular speed of the gondolas if the magnitude of the acceleration of point
A
is not to
exceed 2:5g.
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Dynamics 2e 1167
Problem 6.13
The tractor shown is stuck with its right track off the ground, and therefore the track is able to move
without causing the tractor to move. Letting the diameter of sprocket
A
be
dD2:5 ft
and the diameter of
sprocket Bbe `D2ft, determine the angular speed of sprocket Bif the sprocket Ais rotating at 1rpm.
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Problem 6.14
A battering ram is suspended in its frame with bars
AD
and
BC
, which are identical and pinned at
their endpoints. At the instant shown, point
E
on the ram moves with a speed
v0D15 m=s
. Letting
HD1:75 m and D20ı, determine the magnitude of the angular velocity of the ram at this instant.
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Dynamics 2e 1169
Problem 6.15
A battering ram is suspended in its frame with bars
OA
and
OB
, which
are pinned at
O
. At the instant shown, point
G
on the ram is moving to
the right with a speed
v0D15 m=s
. Letting
HD1:75
m, determine
the angular velocity of the ram at this instant.
Solution
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