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Консультация № 197145
20.11.2019, 02:11
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Тонкий однородный диск массы m = 1 кг и радиуса R может вращаться в вертикальной плоскости вокруг горизонтальной оси, проходящей через его центр С. Под углом а =30 градусов к вертикали в плоскости вращения диска движется маленький пластилиновый шарик такой же массы m со скоростью = 1 м/с. Шарик прилипает к нижней точке неподвижно висящего диска, и система приобретает угловую скорость вращения w. Найти угловую скорость вращения системы после удара, если R = 1 м.
Тонкий однородный диск массы m = 1 кг и радиуса R может вращаться в вертикальной плоскости вокруг горизонтальной оси, проходящей через его центр С. Под углом а =30 градусов к вертикали в плоскости вращения диска движется маленький пластилиновый шарик такой же массы m со скоростью = 1 м/с. Шарик прилипает к нижней точке неподвижно висящего диска, и система приобретает угловую скорость вращения w. Найти угловую скорость вращения системы после удара, если R = 1 м.
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Обсуждение
29.11.2019, 19:36
общий
это ответ
Здравствуйте, dar777!
В момент столкновения с диском пластилинового шарика массы m, движущегося со скоростью v на расстоянии R от оси вращения под углом [$945$] к радиусу, его момент импульса относительно точки C будет равен
Поскольку сам диск в момент столкновения неподвижен, то его момент импульса равен 0, и приведённое выше выражение является общим моментом импульса всей системы (состоящей из диска и шарика).
После столкновения имеем диск радиуса R и массы M = 2m, вращающийся с угловой скоростью [$969$], момент импульса которого равен
Согласно закону сохранения момент импульса замкнутой системы постоянен, то есть
откуда
В данном случае v = 1 м/с, R = 1 м и [$945$] = 30[$186$], поэтому
В момент столкновения с диском пластилинового шарика массы m, движущегося со скоростью v на расстоянии R от оси вращения под углом [$945$] к радиусу, его момент импульса относительно точки C будет равен
Поскольку сам диск в момент столкновения неподвижен, то его момент импульса равен 0, и приведённое выше выражение является общим моментом импульса всей системы (состоящей из диска и шарика).
После столкновения имеем диск радиуса R и массы M = 2m, вращающийся с угловой скоростью [$969$], момент импульса которого равен
Согласно закону сохранения момент импульса замкнутой системы постоянен, то есть
откуда
В данном случае v = 1 м/с, R = 1 м и [$945$] = 30[$186$], поэтому
Форма ответа
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