57
z
H
A
B
a a
Figure 3.30.
Table 3.1
No.
m
1
,
kg
m
2
,
kg
ω
0
,
s
-1
a, m b, m R, m
α,
deg
AO, m
M
z
=
f
1
(t),
N · m
τ, s T, s
OK = s =
f
2
(t – τ), m
1 32 10 -1 1 1.5 1.2 -
πR
6
–29.6 t
2
3 4
5πR
12
(t –τ)
2 200 60 -2 - - 2 120
√3
2
101 5 6
√3 (t – τ)
2
3 120 40 0 2 - - - 0
–120t
4 6
√2
4
(t – τ)
2
4 16 5 -3 - - 1 30 0.4 21t 2 6
0.6√t – τ
5 66 10 1.5 2 1.5 - - 0
15√t 4 6.5
0.5(t – τ)
6 160 80 -1.25 1.5 - 2.5 -
πα
6
-700t √3 2√3
5πa
18
(t – τ)
2
7 300 50 -2 1.6 1 0.8 - 0 968 1 2
πR
2
(t – τ)
2
8 80 20 0 1.2 - 2 -
πα
2
240√t 4 8
πa
4
√t – τ
9 20 5 5 1.2 - 0.4 45
πR
4
-29.2t 3 4
3πR
4
(t – τ)
2
3.1 APPLICATION OF THE ANGULAR MOMENTUM PRINCIPLE TO DETERMINE THE ANGULAR VELOCITY
58 3. TOPIC AK-3
10 100 40 2 2 √2 - -
√2
2
-90√t 4 5
√2
4
(t – τ)
11 60 20 -1 2 - - 15 0 40t 2 4
0.4(t – τ)
2
12 40 10 -3 1 - 2 - 0 50t
2
3 5
πa
3
(t – τ)
13 24 4 4 1 - - - 0.5
-27√t 1 3
0.3(t – τ)
14 40 10 2 - - 1 - 0 120t 1 4
0.5(t – τ)
15 120 50 -4 1 - 2 - 0 330t
2
2 3
πa
2
(t – τ)
2
16 60 10 -5 1 1.2 - 30 0.4 74 2 6
0.3√(t – τ)
17 50 10 -2 - - 1.6 30 0.6 69t 4 6
0.6(t – τ)
18 120 50 3 2 3 0.8 -
πR
2
324 3 5
πR
8
(t – τ)
2
19 90 30 1 1.5 - - - 0 -135t 2 3
πa
4
(t – τ)
20 50 12 3 1 - 1.2 -
πa
6
-14t
2
3 5
πR
12
(t – τ)
2
21 40 10 -6 - - 1 -
√2
2
75√t 1 3
√2
6
(t – τ)
2
22 150 50 -1 1.6 1.2 0.6 -
πR
2
163 4 5
πR
2
(t – τ)
23 90 20 2 √2 1 - -
√3
2
-210 2 3
√3
2
(t – τ)
24 50 12 -3 0.6 - - 60 0.2 27t
2
2 6
0.4√(t – τ)
25 36 8 -5 - - 0.5 - 0 20t 2 4
πR
6
(t – τ)
2
26 150 40 -4 1.5 - 2 -
πa
6
1170√t 1 2
πa
2
(t – τ)
2
27 120 30 0 1 - - 60 0 -25t 2 3
(t – τ)
2
28 15 4 -2 0.6 - - - 0.1 5.6t 3 4
0.4√(t – τ)
29 20 5 5 0.6 - 0.6 - 0
-6.3√t 4 5
5πR
6
(t – τ)
30 150 50 0 1.6 1.2 - - 1.6 652t 2 4
0.2(t – τ)
2
Note: a negative sign of M
z
and ω corresponds to the clockwise direction of the rotation if we look from the positive
side of the axis z.
59
Table 3.2: Axes moments of inertia of homogeneous plates
x
y
z
R
y
z
x
O
mR
2
2
mR
2
4
mR
2
2
R
y
z
x
O
R
y
z
x
O
O
r
m(R
2
+ r
2
)
2
m(R
2
+ r
2
)
4
m(R
2
+ r
2
)
4
R
y
z
x
O
O
r
O
z
y
x
O
a
a
bb
m(a
2
+ b
2
)
2
mb
2
3
ma
2
3
z
y
x
O
a
b
b
z
y
x
O
a
a
ma
2
3
0
ma
2
3
z
y
x
O
a
z
y
x
O
a
a
b/3
O
b
m(3a
2
+ b
2
)
18
mb
2
18
ma
2
6
z
x
O
a
O
b
b/3
y
O
3.1 APPLICATION OF THE ANGULAR MOMENTUM PRINCIPLE TO DETERMINE THE ANGULAR VELOCITY
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.