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969
Chapter 10
Angular Momentum
Conceptual Problems
1
•
True or false:
(
a
)
If two vectors are exactly opposite in direction, their vector product must be
zero.
(
b
)
The magnitude of the vector product of two vectors is at a minimum when
the two vectors are perpendicular.
(
c
)
Knowing the magnitude of the vector product of two nonzero vectors and
the vectors
′
individual magnitudes uniquely determines the angle between
them.
Determine the Concept
The vector product of
A
r
and
B
r
is defined to be
n
B
A
ˆ
sin
φ
AB
=
×
r
r
where
n
ˆ is a unit vector normal to the plane defined by
A
r
and
B
r
and
is the angle between
A
r
and
B
r
.
(
a
) True. If
A
r
and
B
r
are in opposite direction, then sin
=
sin 180
°
= 0
.
(
b
) False. If
A
r
and
B
r
are perpendicular, then sin
=
sin 90
°
= 1 and the vector
product of
A
r
and
B
r
is a maximum.
(
c
) False. Knowing the magnitude of the vector product and the vectors
′
individual
magnitudes only gives the magnitude of the sine of the angle between the vectors.
It does not determine the angle uniquely, nor does this knowledge tell us if the
sine of the angle is positive or negative.
2
•
Consider two nonzero vectors
r
A
and
r
B
. Their vector product has the
greatest magnitude if
r
A
and
r
B
are (
a
) parallel, (
b
) perpendicular, (
c
) antiparallel,
(
d
) at an angle of 45° to each other.
Determine the Concept
The vector product of the vectors
A
r
and
B
r
is defined to
be
n
B
A
ˆ
sin
AB
=
×
r
r
where
n
ˆ is a unit vector normal to the plane defined by
A
r
and
B
r
and
is the angle between
A
r
and
B
r
. Hence, the vector product of
A
r
and
B
r
is a maximum when sin
=
1. This condition is satisfied provided
A
r
and
B
r
are
perpendicular
.
)
(
b
is correct.
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View Full DocumentChapter 10
970
3
•
What is the angle between a force vector
F
r
and a torque vector
τ
r
produced by
F
r
?
Determine the Concept
Because
n
F
r
τ
ˆ
sin
φ
rF
=
×
=
r
r
r
, where
n
ˆ is a unit vector
normal to the plane defined by
r
r
and
F
r
, the angle between
F
r
and
r
is
.
90
°
4
•
A point particle of mass
m
is moving with a constant speed
v
along a
straight line that passes through point
P
. What can you say about the angular
momentum of the particle relative to point
P
? (
a
) Its magnitude is
mv
. (
b
) Its
magnitude is zero. (
c
) Its magnitude changes sign as the particle passes through
point
P
. (
d
) It varies in magnitude as the particle approaches point
P
.
Determine the Concept
L
r
and
p
r
are related according to
p
r
L
r
r
r
×
=
and the
magnitude of
L
r
is
sin
rp
L
=
where
is the angle between
r
r
and
p
r
. Because
the motion is along a line that passes through point
P
,
r
= 0 and so is
L
.
)
(
b
is
correct.
5
•
[SSM]
A particle travels in a circular path and point
P
is at the
center of the circle. (
a
) If the particle’s linear momentum
p
r
is doubled without
changing the radius of the circle, how is the magnitude of its angular momentum
about
P
affected? (
b
) If the radius of the circle is doubled but the speed of the
particle is unchanged, how is the magnitude of its angular momentum about
P
affected?
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 Spring '12
 Goussiou
 Physics, Angular Momentum, Momentum

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