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Консультация № 198094
31.03.2020, 10:43
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05.04.2020, 10:42
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Здравствуйте, 71rus71rus!
В общем случае циклическая частота колебаний физического маятника массой M, центр тяжести которого находится на расстоянии d>0 от оси качания, определяется формулой
где g - ускорение свободного падения, J - момент инерции маятника относительно оси качания.
В данном случае M = 2m = 4 кг, d = 2R = 6 м (центр тяжести системы из двух одинаковых дисков, лежащих в одной плоскости и соединённых в одной точке, расположен в это точке). Чтобы найти момент инерции, воспользуемся тем, что для сплошного диска или цилиндра массой m и радиусом R момент инерции относительно центральной оси равен
а относительно произвольной оси, расположенной параллельно центральной на расстоянии d от неё:
В данном случае центральные оси обоих дисков находятся на расстоянии R и 3R от оси качания, поэтому их моменты инерции относительно неё составят
и
общий же момент инерции маятника относительно оси качания будет равен
кг/м2.
Тогда
рад/с.
В общем случае циклическая частота колебаний физического маятника массой M, центр тяжести которого находится на расстоянии d>0 от оси качания, определяется формулой
где g - ускорение свободного падения, J - момент инерции маятника относительно оси качания.
В данном случае M = 2m = 4 кг, d = 2R = 6 м (центр тяжести системы из двух одинаковых дисков, лежащих в одной плоскости и соединённых в одной точке, расположен в это точке). Чтобы найти момент инерции, воспользуемся тем, что для сплошного диска или цилиндра массой m и радиусом R момент инерции относительно центральной оси равен
а относительно произвольной оси, расположенной параллельно центральной на расстоянии d от неё:
В данном случае центральные оси обоих дисков находятся на расстоянии R и 3R от оси качания, поэтому их моменты инерции относительно неё составят
и
общий же момент инерции маятника относительно оси качания будет равен
кг/м2.Тогда
рад/с.
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