ω - 경상대학교

경상대학교 물리학과 김현수
9-3
1. 회전운동량
L = N
• dt
d
입자계에서회전운동방정식
m i
o
R i
ω
r i
θ i
n
i
i
i
i
i m i
r
ω
v
v
r
L
×
=
•
×
=
좌표계의원점에대한입자계의각운동량
• 어떤
∑
구성입자의회전속도
강체의
[ ]
∑
∑
∑
∑
⋅
−
=
∴
⋅
−
=
⋅
−
⋅
=
×
×
×
×
=
×
=
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
m
m r
r
m
m
)
(
)
(
)
(
)
(
)
(
)
(
2
2
ω
r
r
ω
L
ω
r
r
ω
ω
r
r
r
ω r
r
ω
r
r
ω
r
v
r
L
강체의각운동량
ω
k
j
i
ω
k
k
ω
j
j
ω
i
i
ω
kk
jj
ii
ω
1
kk
jj
ii
1
ω
ω
1
ω
r r
1
ω
r r
ω
L
=
+
+
=
⋅
+
⋅
+
⋅
=
⋅
+
+
=
⋅
+
+
=
=
⋅
⎥ ⋅
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
⎟ −
⎠
⎞
⎜
⎝
⎛
=
⎟ ⋅
⎠
⎞
⎜
⎝
⎛
−
⎟
⎠
⎞
⎜
⎝
⎛
=
•
∑
∑
∑
∑
z
y
x
i
i
i
i
i
i
i
i
i
i
i
i
i
i
m
m r
m
m r
ω
ω
ω
)
(
)
(
)
(
)
(
:
2
2
단위텐서
텐서형태
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
1
0
0
0
1
0
0
0
1
1
)
)(
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
(dyad product)
:
c
b
a
d
c
ab
d
c
b
a
c
ab
c
b
a
c
ab
ab
⋅
⋅
=
⋅
⋅
∗
⋅
=
+
+
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
+
+
+
+
+
+
=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⋅
⋅
=
⋅
•
z
z
y
y
x
x
z
y
x
z
z
y
y
x
x
z
z
z
y
y
x
x
y
z
z
y
y
x
x
x
z
y
x
z
z
y
z
x
z
z
y
y
y
x
y
z
x
y
x
x
x
c
b
c
b
c
b
a
a
a
c
b
c
b
c
b
a
c
b
c
b
c
b
a
c
b
c
b
c
b
a
c
c
c
b
a
b
a
b
a
b
a
b
a
b
a
b
a
b
a
b
a
형태의벡터곱 다이아드 곱
[ ]
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
→
z
z
y
z
x
z
z
y
y
y
x
y
z
x
y
x
x
x
z
y
x
z
y
x
b
a
b
a
b
a
b
a
b
a
b
a
b
a
b
a
b
a
b
b
b
a
a
a
ab