Задача №43.13
Условие
На боковой поверхности круглого цилиндра с вертикальной осью, вокруг которой он может вращаться без трения, вырезан гладкий винтовой желоб с углом подъема α. В начальный момент цилиндр находится в покое; в желоб опускают тяжелый шарик; он падает по желобу без начальной скорости и заставляет цилиндр вращаться. Дано: масса цилиндра M, радиус его R, масса шарика m; расстояние от шарика до оси считаем равным R и момент инерции цилиндра равным MR2/2. Определить угловую скорость ω, которую цилиндр будет иметь в тот момент, когда шарик опустится на высоту h.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
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2.26
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2.28
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2.31
2.32
2.33
2.34
2.35
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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
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2.51
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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
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3.11
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3.13
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3.21
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4.1
4.2
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4.56
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5.1
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6.1
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8.1
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9.1
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10.1
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11.1
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12.1
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13.1
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14.1
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15.1
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16.1
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17.1
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18.1
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19.1
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20.1
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22.1
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23.1
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23.64
23.65
23.66
23.67
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23.71
24.1
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24.34
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25.1
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26.1
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26.35
27.1
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27.4
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27.6
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27.32
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27.34
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27.40
27.41
27.42
27.43
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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29.1
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30.1
30.2
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30.5
30.6
30.7
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30.13
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30.30
31.1
31.2
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31.11
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31.25
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31.32
31.33
31.34
31.35
32.1
32.2
32.3
32.4
32.5
32.6
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32.11
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32.13
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32.15
32.16
32.17
32.18
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32.20
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32.24
32.25
32.26
32.27
32.28
32.29
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32.31
32.32
32.33
32.34
32.35
32.36
32.37
32.38
32.39
32.40
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32.44
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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
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32.64
32.65
32.66
32.67
32.68
32.69
32.70
32.71
32.72
32.73
32.74
32.75
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32.84
32.85
32.86
32.87
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32.89
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32.91
32.92
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32.96
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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
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33.12
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34.1
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34.6
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34.31
35.1
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36.1
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37.1
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37.35
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37.59
38.1
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39.1
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40.1
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41.1
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42.1
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43.1
43.2
43.3
43.4
43.6
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44.1
44.2
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44.4
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45.3
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46.1
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46.32
47.1
47.2
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48.1
48.5
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48.31
48.33
48.34
48.35
48.38
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48.41
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48.44
48.48
48.49
49.1
49.2
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49.8
49.11
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53.5
53.12
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54.1
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54.32
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54.35
55.2
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55.38
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55.44
56.3
56.7
56.9