Задача №37.11
Условие
Вал радиуса r приводится во вращательное движение вокруг горизонтальной оси гирей, подвешенной посредством троса. Для того чтобы угловая скорость вала через некоторое время после начала движения имела величину, близкую к постоянной, с валом соединены n одинаковых пластин; сопротивление воздуха, испытываемое пластиной, приводится к силе, нормальной к пластине, приложенной на расстоянии R от оси вала и пропорциональной квадрату ее угловой скорости, причем коэффициент пропорциональности равен k. Масса гири m, момент инерции всех вращающихся частей относительно оси вращения равен J; массой троса и трением в опорах пренебречь. Определить угловую скорость ω вала, предполагая, что в начальный момент она равна нулю.Решение
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1.1
1.2
1.3
1.4
1.5
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18
2.19
2.20
2.21
2.22
2.23
2.24
2.25
2.26
2.27
2.28
2.29
2.30
2.31
2.32
2.33
2.34
2.35
2.36
2.37
2.38
2.39
2.40
2.41
2.42
2.43
2.44
2.45
2.46
2.47
2.48
2.49
2.50
2.51
2.52
2.53
2.54
2.55
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
3.16
3.17
3.18
3.19
3.20
3.21
3.22
3.23
3.24
3.25
3.26
3.27
3.28
3.29
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3.31
3.32
3.33
3.34
3.35
3.36
3.37
3.38
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
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4.17
4.18
4.19
4.20
4.21
4.22
4.23
4.24
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4.28
4.29
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4.31
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4.33
4.34
4.35
4.36
4.37
4.38
4.39
4.40
4.41
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4.43
4.44
4.45
4.46
4.47
4.49
4.50
4.51
4.52
4.53
4.54
4.55
4.56
4.57
4.58
4.59
4.61
4.62
4.63
4.64
4.65
4.66
4.67
4.68
4.69
4.70
4.71
4.72
4.73
4.74
5.1
5.2
5.3
5.4
5.5
5.6
5.7
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5.12
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5.42
6.1
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7.1
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8.1
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8.31
8.32
8.33
8.34
8.35
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8.37
8.38
8.39
8.40
8.41
8.42
8.43
9.1
9.2
9.3
9.4
9.5
9.6
9.7
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9.10
9.11
9.12
9.13
9.14
9.15
9.16
9.17
9.18
9.19
9.20
9.21
9.22
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9.26
9.27
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
10.11
10.12
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10.14
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10.16
10.17
10.18
10.19
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10.21
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10.23
11.1
11.2
11.3
11.4
11.5
11.6
11.7
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11.10
11.11
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11.17
12.1
12.2
12.3
12.4
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12.10
12.11
12.12
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12.20
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12.33
12.34
12.35
12.36
12.37
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12.40
13.1
13.2
13.3
13.4
13.5
13.6
13.7
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13.20
14.1
14.2
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15.1
15.3
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16.1
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16.5
16.6
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16.37
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16.41
17.1
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17.11
18.1
18.2
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18.4
18.5
18.6
18.7
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18.11
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18.33
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18.35
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18.37
18.38
18.39
18.40
18.41
19.1
19.2
19.3
19.4
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19.6
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19.11
19.12
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19.14
19.15
20.1
20.2
20.3
20.4
20.5
20.6
20.7
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20.13
20.14
20.15
20.16
20.17
20.18
21.2
21.3
21.4
21.5
21.6
21.7
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21.13
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21.15
22.1
22.2
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22.24
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22.26
22.27
23.1
23.2
23.3
23.4
23.5
23.6
23.7
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23.10
23.11
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23.15
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23.20
23.21
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23.26
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23.28
23.29
23.30
23.31
23.32
23.33
23.34
23.35
23.36
23.37
23.38
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23.40
23.41
23.42
23.43
23.44
23.45
23.46
23.47
23.48
23.49
23.50
23.51
23.52
23.53
23.54
23.55
23.56
23.57
23.58
23.59
23.60
23.61
23.62
23.63
23.64
23.65
23.66
23.67
23.68
23.69
23.70
23.71
24.1
24.2
24.3
24.4
24.5
24.6
24.7
24.8
24.9
24.10
24.11
24.12
24.13
24.14
24.15
24.16
24.18
24.19
24.20
24.21
24.22
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24.24
24.25
24.26
24.27
24.28
24.29
24.30
24.31
24.34
24.35
24.36
24.37
24.38
24.39
24.40
24.41
24.42
24.43
24.44
24.45
24.46
25.1
25.2
25.3
25.4
25.5
25.7
25.9
25.10
25.11
25.12
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25.14
25.16
25.17
25.18
26.1
26.2
26.3
26.4
26.5
26.6
26.7
26.8
26.9
26.10
26.11
26.12
26.13
26.14
26.15
26.16
26.17
26.18
26.19
26.20
26.21
26.22
26.23
26.24
26.25
26.26
26.27
26.28
26.29
26.30
26.31
26.32
26.33
26.34
26.35
27.1
27.2
27.3
27.4
27.5
27.6
27.7
27.8
27.9
27.10
27.11
27.12
27.13
27.14
27.15
27.16
27.17
27.18
27.19
27.20
27.21
27.22
27.23
27.24
27.25
27.26
27.27
27.28
27.29
27.30
27.32
27.33
27.34
27.35
27.36
27.37
27.38
27.39
27.40
27.41
27.42
27.43
27.44
27.45
27.46
27.47
27.48
27.49
27.50
27.51
27.52
27.54
27.55
27.58
27.59
27.60
27.61
27.62
27.63
27.64
27.65
28.1
28.2
28.3
28.4
28.5
28.6
28.7
28.8
28.9
28.10
28.11
28.12
28.13
28.14
28.15
28.16
28.17
28.18
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28.20
28.21
28.22
29.1
29.2
29.3
29.4
29.5
29.6
29.7
29.8
29.9
29.10
29.11
29.12
29.13
29.14
29.15
29.16
30.1
30.2
30.3
30.4
30.5
30.6
30.7
30.8
30.9
30.10
30.11
30.12
30.13
30.14
30.15
30.16
30.17
30.18
30.19
30.20
30.21
30.22
30.23
30.24
30.25
30.26
30.27
30.28
30.29
30.30
31.1
31.2
31.3
31.4
31.5
31.6
31.7
31.8
31.9
31.11
31.13
31.14
31.15
31.16
31.17
31.18
31.19
31.20
31.21
31.22
31.23
31.25
31.26
31.27
31.28
31.29
31.30
31.31
31.32
31.33
31.34
31.35
32.1
32.2
32.3
32.4
32.5
32.6
32.7
32.8
32.9
32.10
32.11
32.12
32.13
32.14
32.15
32.16
32.17
32.18
32.19
32.20
32.21
32.22
32.23
32.24
32.25
32.26
32.27
32.28
32.29
32.30
32.31
32.32
32.33
32.34
32.35
32.36
32.37
32.38
32.39
32.40
32.41
32.42
32.43
32.44
32.45
32.46
32.47
32.48
32.49
32.50
32.51
32.52
32.53
32.54
32.55
32.56
32.57
32.58
32.59
32.60
32.61
32.62
32.63
32.64
32.65
32.66
32.67
32.68
32.69
32.70
32.71
32.72
32.73
32.74
32.75
32.76
32.77
32.79
32.80
32.81
32.82
32.83
32.84
32.85
32.86
32.87
32.88
32.89
32.90
32.91
32.92
32.93
32.94
32.95
32.96
32.97
32.98
32.99
32.100
32.101
32.102
32.103
32.104
32.105
32.106
32.107
33.1
33.2
33.3
33.4
33.5
33.6
33.8
33.9
33.10
33.11
33.12
33.13
33.14
33.15
33.16
33.17
33.18
33.19
33.20
33.21
33.22
34.1
34.2
34.3
34.4
34.5
34.6
34.7
34.8
34.9
34.10
34.11
34.12
34.13
34.14
34.15
34.16
34.17
34.18
34.19
34.20
34.21
34.22
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34.24
34.25
34.26
34.27
34.28
34.29
34.30
34.31
35.1
35.2
35.3
35.4
35.5
35.6
35.7
35.8
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35.10
35.11
35.12
35.13
35.14
35.15
35.16
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35.18
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35.21
36.1
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36.11
36.12
36.13
36.14
37.1
37.2
37.3
37.4
37.5
37.6
37.7
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37.11
37.12
37.13
37.14
37.15
37.16
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37.23
37.25
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37.32
37.33
37.34
37.35
37.36
37.37
37.38
37.39
37.40
37.41
37.42
37.43
37.44
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37.46
37.47
37.48
37.49
37.50
37.51
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37.53
37.54
37.55
37.56
37.57
37.58
37.59
38.1
38.2
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38.5
38.6
38.7
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38.11
38.12
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38.17
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38.24
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38.26
38.27
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38.29
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38.31
38.32
38.33
38.34
38.35
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38.37
38.38
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38.42
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38.53
39.1
39.2
39.4
39.5
39.6
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39.12
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39.14
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39.22
40.1
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40.6
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41.1
41.2
41.3
41.4
41.5
41.6
41.7
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41.10
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41.12
41.13
41.14
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41.18
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41.23
42.1
42.2
42.3
42.4
42.5
42.6
42.7
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42.18
43.1
43.2
43.3
43.4
43.6
43.7
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43.13
44.1
44.2
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44.4
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44.6
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44.29
45.3
45.4
45.5
45.6
45.7
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45.34
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45.37
46.1
46.2
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46.5
46.6
46.7
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46.21
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46.31
46.32
47.1
47.2
47.3
47.4
47.5
47.6
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47.19
48.1
48.5
48.6
48.7
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48.12
48.13
48.14
48.15
48.19
48.23
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48.26
48.27
48.28
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48.31
48.33
48.34
48.35
48.38
48.40
48.41
48.42
48.43
48.44
48.48
48.49
49.1
49.2
49.3
49.4
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49.8
49.11
49.12
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49.15
49.16
53.5
53.12
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53.16
54.1
54.2
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54.5
54.6
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54.18
54.19
54.20
54.22
54.32
54.33
54.35
55.2
55.3
55.4
55.5
55.6
55.7
55.8
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55.12
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55.16
55.21
55.25
55.38
55.41
55.44
56.3
56.7
56.9