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Консультация № 185853
18.04.2012, 06:31
74.26 руб.
0
5
1
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Однородный тонкий стержень длиной L вращается вокруг гладкой горизонтальной оси O. В момент начала движения стержень находится в горизонтальном положении, и стержень начинает двигаться из состояния покоя.
Найти угловое ускорение стержня в момент, когда он находился в горизонтальном положении, β=?
Найти угловую скорость стержня в момент, когда он достигнет угла θ, ω=?
Нарисовать рисунок.
Однородный тонкий стержень длиной L вращается вокруг гладкой горизонтальной оси O. В момент начала движения стержень находится в горизонтальном положении, и стержень начинает двигаться из состояния покоя.
Найти угловое ускорение стержня в момент, когда он находился в горизонтальном положении, β=?
Найти угловую скорость стержня в момент, когда он достигнет угла θ, ω=?
Нарисовать рисунок.
Обсуждение
18.04.2012, 07:00
общий
это ответ
Здравствуйте, Arman Muratuly!
В принципе, всё нужное для решения было сказано в предыдущей задаче. И рисунок вы нарисовали хороший. Итак.
Сумма кинетической и потенциальной энергий постоянна:
.
.
Откуда искомая угловая скорость
.
Угловое ускорение получим, продифференцировав по времени выражение для квадрата угловой скорости:
Откуда
.
Нас интересует ускорение в начальный момент, когда стержень горизонтален, т.е.
:
.
Заметим, что угловое ускорение отрицательно, как и должно быть - угол уменьшается, и скорость его уменьшения(угловая скорость) растёт.
В принципе, всё нужное для решения было сказано в предыдущей задаче. И рисунок вы нарисовали хороший. Итак.
Сумма кинетической и потенциальной энергий постоянна:
..Откуда искомая угловая скорость
.Угловое ускорение получим, продифференцировав по времени выражение для квадрата угловой скорости:
Откуда
.Нас интересует ускорение в начальный момент, когда стержень горизонтален, т.е.
:.Заметим, что угловое ускорение отрицательно, как и должно быть - угол уменьшается, и скорость его уменьшения(угловая скорость) растёт.
Неизвестный
19.04.2012, 04:23
общий
я не совсем понял, для угловой скорости чему равен θ0 ?
θ0 = pi/2 ?
θ0 = pi/2 ?
- начальный угол.
Форма ответа
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