10
Rotation of a Rigid Object
About a Fixed Axis
CHAPTER OUTLINE
10.1
Angular Position, Velocity,
and Acceleration
10.2
Rotational Kinematics: Rotational
Motion with Constant Angular
Acceleration
10.3
Angular and Translational
Quantities
10.4
Rotational Energy
10.5
Calculation of Moments of Inertia
10.6
Torque
10.7
Relationship Between Torque and
Angular Acceleration
10.8
Work, Power, and Energy in
Rotational Motion
10.9
Rolling Motion of a Rigid Object
ANSWERS TO QUESTIONS
Q10.1
1 rev
/
min, or
π
30
rad
/
s. The direction is horizontally into
the wall to represent clockwise rotation. The angular
velocity is constant so
α
=
0.
Q10.2
The vector angular velocity is in the direction
+
ˆ
k
. The vector angular acceleration has the
direction
−
ˆ
k
.
*Q10.3
(i)
answer (a). Smallest
I
is about
x
axis, along which the largermass balls lie.
(ii)
answer (c). The balls all lie at a distance from the
z
axis, which is perpendicular to both the
x
and
y
axes and passes through the origin.
*Q10.4
(i)
answer (d). The speedometer measures the number of revolutions per second of the tires.
A larger tire will travel more distance in one full revolution as 2
r
.
(ii)
answer (c). If the driver uses the gearshift and the gas pedal to keep the tachometer readings
and the air speeds comparable before and after the tire switch, there should be no effect.
*Q10.5
The accelerations are not equal, but greater in case (a). The string tension above the 5.1kg object
is less than its weight while the object is accelerating down.
Q10.6
The object will start to rotate if the two forces act along different lines. Then the torques of the
forces will not be equal in magnitude and opposite in direction.
Q10.7
The angular speed
ω
would decrease. The center of mass is farther from the pivot, but the
moment of inertia increases also.
Q10.8
You could use
ωα
=
t
and
v
=
at
. The equation
v
=
R
is valid in this situation since
aR
=
.
215
FIG. Q10.1
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View Full DocumentQ10.9
The moment of inertia depends on the distribution of mass with respect to a given axis. If the axis
is changed, then each bit of mass that makes up the object is a different distance from the axis. In
an example in section 10.5 in the text, the moment of inertia of a uniform rigid rod about an axis
perpendicular to the rod and passing through the center of mass is derived. If you spin a pencil back
and forth about this axis, you will get a feeling for its stubbornness against changing rotation. Now
change the axis about which you rotate it by spinning it back and forth about the axis that goes
down the middle of the graphite. Easier, isn’t it? The moment of inertia about the graphite is much
smaller, as the mass of the pencil is concentrated near this axis.
Q10.10
A quick ﬂ
ip will set the hard–boiled egg spinning faster and more smoothly. Inside the raw egg,
the yolk takes some time to start rotating. The raw egg also loses mechanical energy to internal
ﬂ
uid friction.
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 Fall '08
 NianLin
 Physics, Acceleration, Energy, Kinetic Energy, Moment Of Inertia, Ω, θ

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