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Problem 7.37
The composite body lies in the vertical plane and is rotating with angular
speed
!bD11 rad=s
at the instant shown. The mass of the disk
D
is
mbD4kg
, the mass of the bar
AB
is
mAB D1:5 kg
, the length of the
bar
AB
is
LD50 cm
, and the radius of the disk is
RD10 cm
. At the
instant shown, determine the angular acceleration of the composite body
and the horizontal and vertical reactions on the body at A.
2mbg.L CR/ DIC˛AB CIE˛DCmAB aCy L
2CmbaEy .L CR/; (3)
where the mass moments of inertia are given by
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 1487
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 7.38
The bar
AB
is pinned to a fixed support at
A
at one end and to
the center of the bike wheel
B
at its other end. The bike wheel
is spinning with angular speed
!0D50 rad=s
when it is gently
placed on the horizontal surface. The mass of the bike wheel is
mwD2:5 kg
, its radius is
RD33 cm
, and its mass moment of
inertia is IBD0:2486 kgm2.
If the mass of bar
AB
is negligible and the coefficient of kinetic
friction between the wheel and the surface is
kD0:6
, determine
the time it takes for the wheel to come to a complete stop, and find
the reactions at Aand Bon bar AB.
fFAB
p2DmwaBx;
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 1489
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 7.39
The bar
AB
is pinned to a fixed support at
A
at one end and to
the center of the bike wheel
B
at its other end. The bike wheel
is spinning with angular speed
!0D50 rad=s
when it is gently
placed on the horizontal surface. The mass of the bike wheel is
mwD2:5 kg
, its radius is
RD33 cm
, and its mass moment of
inertia is IBD0:2486 kgm2.
If the mass of bar
AB
is
mAB D1:5 kg
and the coefficient of
kinetic friction between the wheel and the surface is
kD0:6
,
determine the time it takes for the wheel to come to a complete stop,
and find the reactions at Aand Bon bar AB.
Solution
Since bar
AB
has mass, the FBD of the bar and of the wheel are as shown on
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 1491
Computation. Substituting the kinematics equations and the force law in to Eqs. (1)–(6), we obtain
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 7.40
The bar
AB
is pinned to a fixed support at
A
at one end and to
the center of the bike wheel
B
at its other end. The bike wheel
is spinning with angular speed
!0D50 rad=s
when it is gently
placed on the horizontal surface. The mass of the bike wheel is
mwD2:5 kg
, its radius is
RD33 cm
, and its mass moment of
inertia is IBD0:2486 kgm2.
If the mass of bar
AB
is
mAB D1:5 kg
, determine the coefficient
of kinetic friction between the wheel and the surface so that it takes
2
s to come to a complete stop. In addition, find the reactions at
A
and Bon bar AB for these conditions.
Solution
Since bar
AB
has mass, the FBD of the bar and of the wheel are as shown on
the right, where
F
f
is the friction force between the wheel and the ground and
Cis the mass center of bar AB.
Balance Principles.
Using the FBDs on the right, the Newton-Euler equa-
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 1493
Computation. Substituting the kinematics equations and the force law in to Eqs. (1)–(6), we obtain
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 7.41
Assume that the plane is on the ground, and model each of its two
propeller blades as a rectangular plate of mass
mD29 kg
, length
LD137 cm
, and width
wD20 cm
. If the engine torque
MO
applied to the propeller shaft is
410 Nm
, determine the time it
takes for the blades to achieve an angular speed of
2000 rpm
if the
blades start from rest. What would be the required time if, instead,
the blades were modeled as thin rods of length Land mass m?
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1495
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.
