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Консультация № 196659
12.10.2019, 20:16
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
1.Горизонтально расположенное кольцо массой m, с внутренним и внешним радиусами R и 2R соответственно, равномерно вращается вокруг вертикальной оси, касаясь её своей внутренней стороной. Наибольшая скорость, которой обладает одна из точек кольца, равна υ. Чему равен момент импульса кольца относительно оси вращения?
1.Горизонтально расположенное кольцо массой m, с внутренним и внешним радиусами R и 2R соответственно, равномерно вращается вокруг вертикальной оси, касаясь её своей внутренней стороной. Наибольшая скорость, которой обладает одна из точек кольца, равна υ. Чему равен момент импульса кольца относительно оси вращения?
Обсуждение
13.10.2019, 11:44
общий
это ответ
Здравствуйте, dar777!
Дано: m -- масса кольца; R -- внутренний радиус кольца и расстояние от оси Z симметрии кольца до оси z вращения; 2R -- внешний радиус кольца; v -- наибольшая окружная скорость точки кольца.
Определить: Lz -- момент импульса кольца относительно оси вращения.
Решение
Рисунок к задаче находится в прикреплённом файле. Имеем
r=R+2R=3R -- расстояние от оси вращения кольца до точки, окружная скорость которой наибольшая;
[$969$]=v/r=v/(3R) -- угловая скорость кольца [1, с. 66];
JZ=m(R2+(2R)2)/2=5mR2/2 -- момент инерции кольца относительно оси Z [1, с. 98];
Jz=JZ+mR2=5mR2/2+mR2=7mR2/2 -- момент инерции кольца относительно оси z [1, с. 99];
Lz=Jz[$969$]=(7mR2/2)*(v/(3R))=7mvR/6 -- искомый момент импульса [1, с. 104].
Ответ: 7mvR/6.
Литература
1. Кухлинг Х. Справочник по физике. -- М.: Мир, 1985. -- 520 с.
Дано: m -- масса кольца; R -- внутренний радиус кольца и расстояние от оси Z симметрии кольца до оси z вращения; 2R -- внешний радиус кольца; v -- наибольшая окружная скорость точки кольца.
Определить: Lz -- момент импульса кольца относительно оси вращения.
Решение
Рисунок к задаче находится в прикреплённом файле. Имеем
r=R+2R=3R -- расстояние от оси вращения кольца до точки, окружная скорость которой наибольшая;
[$969$]=v/r=v/(3R) -- угловая скорость кольца [1, с. 66];
JZ=m(R2+(2R)2)/2=5mR2/2 -- момент инерции кольца относительно оси Z [1, с. 98];
Jz=JZ+mR2=5mR2/2+mR2=7mR2/2 -- момент инерции кольца относительно оси z [1, с. 99];
Lz=Jz[$969$]=(7mR2/2)*(v/(3R))=7mvR/6 -- искомый момент импульса [1, с. 104].
Ответ: 7mvR/6.
Литература
1. Кухлинг Х. Справочник по физике. -- М.: Мир, 1985. -- 520 с.
Прикрепленные файлы:
5
Это самое лучшее решение!
Об авторе:
Facta loquuntur.
Facta loquuntur.
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