Задача №48.23

Условие

Материальная точка M движется под действием силы тяжести по прямолинейному стержню AB, вращающемуся с постоянной угловой скоростью ω вокруг неподвижной вертикальной оси. Стержень AB образует угол α с горизонталью. Найти закон движения точки.

Решение




Предыдущая задача №22
Концы однородного тяжелого стержня AB длины 2a и массы M скользят без трения по горизонтальному и вертикальному стержням рамки, вращающейся с постоянной угловой скоростью ω вокруг вертикальной стороны. Составить уравнение движения стержня и определить положение относительного равновесия.
Следующая задача №24
Материальная точка массы m движется по круговой рамке радиуса a, которая вращается с постоянной угловой скоростью ω вокруг вертикального диаметра AB. Составить уравнение движения точки и определить момент M, необходимый для поддержания постоянства угловой скорости.
Источник: Решебник Мещерского 12 класс
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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
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2.20
2.21
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2.24
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2.34
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2.43
2.44
2.45
2.46
2.47
2.48
2.49
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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
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3.19
3.20
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4.1
4.2
4.3
4.4
4.5
4.6
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4.10
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4.12
4.13
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4.49
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4.51
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4.53
4.54
4.55
4.56
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4.61
4.62
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4.65
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4.69
4.70
4.71
4.72
4.73
4.74
5.1
5.2
5.3
5.4
5.5
5.6
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5.42
6.1
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6.4
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6.6
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7.1
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7.6
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8.1
8.2
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8.43
9.1
9.2
9.3
9.4
9.5
9.6
9.7
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9.10
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9.12
9.13
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9.27
10.1
10.2
10.3
10.4
10.5
10.6
10.7
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11.1
11.2
11.3
11.4
11.5
11.6
11.7
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12.1
12.2
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12.4
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12.6
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13.1
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14.1
14.2
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15.1
15.3
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16.1
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16.41
17.1
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18.1
18.2
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18.41
19.1
19.2
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20.1
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20.13
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21.2
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22.1
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23.1
23.2
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23.48
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23.62
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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
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24.31
24.34
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24.44
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24.46
25.1
25.2
25.3
25.4
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26.1
26.2
26.3
26.4
26.5
26.6
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26.34
26.35
27.1
27.2
27.3
27.4
27.5
27.6
27.7
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27.10
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27.20
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27.32
27.33
27.34
27.35
27.36
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27.44
27.45
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27.47
27.48
27.49
27.50
27.51
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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
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28.22
29.1
29.2
29.3
29.4
29.5
29.6
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30.1
30.2
30.3
30.4
30.5
30.6
30.7
30.8
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30.10
30.11
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30.30
31.1
31.2
31.3
31.4
31.5
31.6
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31.8
31.9
31.11
31.13
31.14
31.15
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31.20
31.21
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31.25
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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
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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
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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
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32.40
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32.44
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32.46
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32.48
32.49
32.50
32.51
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32.53
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32.55
32.56
32.57
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32.59
32.60
32.61
32.62
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32.64
32.65
32.66
32.67
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32.69
32.70
32.71
32.72
32.73
32.74
32.75
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32.77
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32.80
32.81
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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
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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
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33.12
33.13
33.14
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33.16
33.17
33.18
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33.22
34.1
34.2
34.3
34.4
34.5
34.6
34.7
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34.10
34.11
34.12
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34.14
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34.30
34.31
35.1
35.2
35.3
35.4
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36.1
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37.1
37.2
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37.4
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37.11
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37.25
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37.38
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37.48
37.49
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37.53
37.54
37.55
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37.59
38.1
38.2
38.3
38.4
38.5
38.6
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38.38
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38.53
39.1
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39.4
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39.6
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39.22
40.1
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41.1
41.2
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41.4
41.5
41.6
41.7
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41.12
41.13
41.14
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41.23
42.1
42.2
42.3
42.4
42.5
42.6
42.7
42.8
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42.11
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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
44.3
44.4
44.5
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
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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
47.7
47.8
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47.10
47.11
47.12
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47.15
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47.18
47.19
48.1
48.5
48.6
48.7
48.9
48.10
48.12
48.13
48.14
48.15
48.19
48.23
48.24
48.26
48.27
48.28
48.29
48.30
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
49.7
49.8
49.11
49.12
49.13
49.14
49.15
49.16
53.5
53.12
53.14
53.15
53.16
54.1
54.2
54.3
54.4
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
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55.9
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55.11
55.12
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55.21
55.25
55.38
55.41
55.44
56.3
56.7
56.9
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