AngularMomentum
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Angular Momentum and Inertia in Rotating Systems, Slides of Classical Mechanics
The concepts of angular momentum and inertia in rotating systems. It covers the definition of moments, shifted moments, and the law of angular inertia. The document also introduces the concept of a rigid body and angular velocity. Additionally, it discusses the definition of angular momentum in terms of inertia and angular velocity, and the representation of rotational inertia by an inertia tensor.
Typology: Slides
2012/2013
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Angular
Momentum
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Moments
The
moment
of
a
vector
at
a
point
is
the
wedge
product.
This
is
applied
to
physical
variables
in
rotating
systems.
Applied
to
momentum
for
angular
momentum
Applied
to
force
for
torque
Moments
are
summed
for
systems
of
particles.
x
1
x
2
x
3
k
j
ijk
i
A
x
A
r
r
A
F
r
N
p
r
J
J
J
N
N
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Law
of
Angular
Inertia
The
time
derivative
of
angular
momentum
vector
is
the
net
torque
vector.
By
the
law
of
reaction,
all
internal
torques
come
in
canceling
pairs.
Only
need
external
torques
N
F
r
dt
J
d
v
m
v
F
r
dt
J
d
p
dt
r
d
dt
p
d
r
dt
J
d
)
(
)
(
)
(
)
(
)
(
)
(
ext
int
ext
F
r
dt
J
d
F
r
F
r
dt
J
d
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Rigid
Body
If
the
positions
of
separate
masses
are
fixed
compared
to
the
center
of
mass
it
is
a
rigid
body
Rigid
body
motion
can
be
expressed
in
terms
of
the
center
of
mass.
Translational
motion
Rotational
motion
r
r
v
CM
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Angular
Momentum
The
angular
momentum
can
be
defined
in
terms
of
the
inertia
and
angular
velocity.
Accounts
for
non
‐
collinear
vectors
J
r
p
j
ij
i
I
J
)
(
,
,
,
,
j
i
ij
k
k
ij
x x x x m I
r r m p r J
r
r
r
m
J
2
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Inertia
Tensor
Rotational
inertia
is
represented
by
a
tensor.
Symmetric
tensor
Diagonal
elements
are
moments
of
inertia
Off
‐
diagonal
are
products
of
inertia
)
(
2
3
,
2
2
,
x
x
m
A
)
(
2
3
,
2
1
,
x
x
m
B
)
(
2
2
,
2
1
,
x
x
m
C
C
F
G
F
B
H
G
H
A
I
)
(
,
,
,
,
j
i
ij
k
k
ij
x x x x m I
3
,
2
,
x
x
m
F
3
,
1
,
x
x
m
G
2
,
1
,
x
x
m
H
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