CHAPTER
9
ROTATIONAL DYNAMICS
CONCEPTUAL QUESTIONS
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1.
REASONING AND SOLUTION
The magnitude of the torque produced by a force
F
is
given by the magnitude of the force times the lever arm. When a long pipe is slipped over a
wrench handle, the length of the wrench handle is effectively increased. The same force can
then be applied with a larger lever arm. Therefore, a greater torque can be used to remove
the "frozen" nut.
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2.
REASONING AND SOLUTION
The torque produced by a force
F
is given by
τ
=
F
A
where
is the lever arm.
A
a. A large force can be used to produce a small torque by choosing a small lever arm.
Then
the product
is small even though the magnitude of the force,
F
, is large. If the line of
action passes through the axis of rotation,
= 0 m, and the torque is zero regardless of how
large
F
is.
F
A
A
b. A small force may be used to produce a large torque by choosing a large lever arm
Then, the product
can be large even though the magnitude of the force
F
is small.
A
.
F
A
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3.
REASONING AND SOLUTION
In a cassette deck, the magnetic tape applies a torque to
the supply reel. The magnitude of the torque is equal to the product of the tension
F
T
in the
tape, assumed to be constant, and the lever arm
. As shown below, the lever arm is the
radius of the tape remaining on the supply reel. Figure A shows the reel and tape at an
earlier time; figure B shows the tape and the reel at a later time.
A
A
F
T
A
F
T
Figure A
Figure B
As the reel becomes empty, the lever arm
gets smaller, as suggested in the figures above.
Therefore, the torque exerted on the reel by the tape becomes smaller.
A
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Conceptual Questions
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4.
REASONING AND SOLUTION
A flat rectangular sheet of plywood is fixed so that it can
rotate about an axis perpendicular to the sheet through one corner, as shown in the figure. In
order to produce the largest possible torque with the force
F
(acting in the plane of the
paper), the force
F
must be applied with the largest possible lever arm. This can be attained
by orienting the force
F
so that it is perpendicular to the diagonal that passes through the
rotation axis as shown below. The lever arm is equal to the length of the diagonal of the
plywood.
Axis of
rotation
F
A
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5.
REASONING AND SOLUTION
To unscrew either cap, you apply a force tangentially to it
and rotate it about an axis perpendicular to the end of the cap at its center.
It is the torque
created by this force that turns the cap.
The greater the torque, the more easily is the cap
unscrewed.
For a given force, a greater torque is created when the force has a greater lever
arm than when it has a smaller lever arm.
In the case of the two caps, the lever arms are the
radii of the caps, and the “easyoff” cap has a greater radius than the normal cap.
Thus, it is
the greater radius of the “easyoff” cap that makes it easier to open.
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 Spring '08
 holland
 Angular Momentum, Force, Moment Of Inertia, Rotation, Rotational Dynamics

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