CHAPTER
8
ROTATIONAL KINEMATICS
CONCEPTUAL QUESTIONS
____________________________________________________________________________________________
1.
REASONING AND SOLUTION
The figures below show two axes in the plane of the
paper and located so that the points
B
and
C
move in circular paths having the same radii
(radius =
r
).
A
B
C
r
r
Axis
A
B
C
r
r
Axis
____________________________________________________________________________________________
2.
REASONING AND SOLUTION
When a pair of scissors is used to cut a string, each blade
of the scissors does not have the same angular velocity at a given instant during the cut. The
angular speed of each blade is the same; however, each blade rotates in the opposite
direction. Therefore, it is correct to conclude that the blades have opposite angular velocities
at any instant during the cut.
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ROTATIONAL KINEMATICS
3.
REASONING AND SOLUTION
Just before the battery is removed, the second hand is
rotating so that its angular velocity is clockwise. The second hand moves with a constant
angular velocity, so the angular acceleration is zero. When the battery is removed, the
second hand will continue to rotate with its clockwise angular velocity, but it will slow
down. Therefore, the angular acceleration must be opposite to the angular velocity, or
counterclockwise.
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4.
REASONING AND SOLUTION
The tangential speed,
v
T
, of a point on the earth's surface
is related to the earth's angular speed
ϖ
according to
T
v
r
ϖ
=
, Equation 8.9, where
r
is the
perpendicular distance from the point to the earth's rotation axis. At the equator,
r
is equal to
the earth's radius. As one moves away from the equator toward the north or south
geographic pole, the distance
r
becomes smaller. Since the earth's rotation axis passes
through the geographic poles,
r
is effectively zero at those locations. Therefore, your
tangential speed would be a minimum if you stood as close as possible to either the north or
south geographic pole.
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5.
SSM
REASONING AND SOLUTION
a. A thin rod rotates at a constant angular speed about an axis of rotation that is
perpendicular to the rod at its center. As the rod rotates, each point at a distance
r
from the
center on one half of the rod has the same tangential speed as the point at a distance
r
from
the center on the other half of the rod. This is true for all values of
r
for
0
<
r
≤
(
L
/2)
where
L
is the length of the rod.
b.
If the rod rotates about an axis that is perpendicular to the rod at one end, no two points
are the same distance from the axis of rotation.
Therefore, no two points on the rod have the
same tangential speed.
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6.
REASONING AND SOLUTION
The wheels are rotating with a constant angular velocity.
a. Since the angular velocity is constant, each wheel has zero angular acceleration,
α
= 0 rad/s. Since the tangential acceleration
a
T
is related to the angular acceleration through
Equation 8.10,
T
a
r
α
=
, every point on the rim has zero tangential acceleration.
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 Spring '07
 Russell
 Physics, Acceleration, Angular velocity, Velocity, rad/s

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