Physics for Scientists and Engineers, 6e
Chapter 11 - Angular Momentum
Which of the following is equivalent to the
following scalar product: (A × B) · (B × A)?
1.
2.
3.
4.
A·B+B·A
(A × A) · (B × B)
(A × B) · (A × B)
-(A × B) · (A × B)
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This result can be obtained by replacing B × A with (A × B), according to Equation 11.4.
Which of the following statements is true about the
relationship between the magnitude of the cross
product of two vectors and the product of the
magnitudes of the vectors?
1.
2.
3.
4.
|A × B| is larger than AB
|A × B| is smaller than AB
|A × B| could be larger or
smaller than AB,
depending on the angle
between the vectors
|A × B| could be equal to
AB
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Because of the sin θ function, |A × B| is either equal to
or smaller than AB, depending on the angle θ.
Recall the skater described at the beginning of
section 11.2 (see figure). Let her mass be m. What
would be her angular momentum relative to the pole
at the instant she is a distance d from the pole if she
were skating directly toward it at speed v?
1.
2.
3.
33%
zero
mvd
impossible to determine
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33%
33%
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3
If p and r are parallel or antiparallel, the
angular momentum is zero. For a nonzero
angular momentum, the linear momentum
vector must be offset from the rotation axis.
Consider again the skater in question 3. What would
be her angular momentum relative to the pole at the
instant she is a distance d from the pole if she were
skating at speed v along a straight line that would
pass within a distance a from the pole?
1.
2.
3.
4.
25% 25% 25% 25%
zero
mvd
mva
impossible to determine
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The angular momentum is the product of the linear
momentum and the perpendicular distance from the
rotation axis to the line along which the linear
momentum vector lies.
A solid sphere and a hollow sphere have the
same mass and radius. They are rotating with
the same angular speed. The one with the
higher angular momentum is
1.
2.
3.
4.
the solid sphere
the hollow sphere
They both have the same
angular momentum.
impossible to determine
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The hollow sphere has a larger moment of inertia
than the solid sphere.
A competitive diver leaves the diving board and falls
toward the water with her body straight and rotating
slowly. She pulls her arms and legs into a tight tuck
position. Her angular speed
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2.
3.
4.
increases
decreases
stays the same
is impossible to determine
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The diver is an isolated system, so
the product Iω remains constant.
Because her moment of inertia
decreases, her angular speed
increases.
Consider the competitive diver in question 6 again.
When she goes into the tuck position, the rotational
kinetic energy of her body
1.
2.
3.
4.
increases
decreases
stays the same
is impossible to determine
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As the moment of inertia of the diver
decreases, the angular speed increases
by the same factor. For example, if I
goes down by a factor of 2, ω goes up
by a factor of 2. The rotational kinetic
energy varies as the square of ω. If I is
halved, ω2 increases by a factor of 4
and the energy increases by a factor of
2