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Консультация № 194119
07.12.2018, 01:09
0.00 руб.
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Здравствуйте! У меня возникли сложности с таким вопросом:
Найти момент инерции прямоугольного треугольника
массой m = 6 кг относительно оси, совпадающей с одним из его
катетов, если другой катет a = 60 см.
Найти момент инерции прямоугольного треугольника
массой m = 6 кг относительно оси, совпадающей с одним из его
катетов, если другой катет a = 60 см.
Обсуждение
10.12.2018, 10:38
общий
Адресаты:
Вы полностью и правильно сообщили условие задачи?
Об авторе:
Facta loquuntur.
Facta loquuntur.
10.12.2018, 15:28
общий
это ответ
Здравствуйте, lenocvol!
Пусть длина катета, вокруг которого происходит вращение, b, а поверхностная плотность треугольника [$963$]
На расстоянии 0[$8804$]r[$8804$]a от оси длина узкой полосы параллельной оси равна
x=b(1-r/a)
площадь этой полосы при ширине dr равна
dS=x dr=b(1-r/a) dr
Её масса
dm=[$963$] dS=[$963$]b(1-r/a) dr
и момент инерции
dJ=r2dm=[$963$]b(r2-r3/a) dr
Интегрируем
J=0a[$8747$][$963$]b(r2-r3/a) dr=[$963$]b(a3/3-a4/4a)=[$963$]ba3/12
Но масса треугольника
m=[$963$]ab/2
откуда
J= ma2/6=6кг[$183$](0,6м)2/6=0,36 кг[$183$]м2
Пусть длина катета, вокруг которого происходит вращение, b, а поверхностная плотность треугольника [$963$]
На расстоянии 0[$8804$]r[$8804$]a от оси длина узкой полосы параллельной оси равна
x=b(1-r/a)
площадь этой полосы при ширине dr равна
dS=x dr=b(1-r/a) dr
Её масса
dm=[$963$] dS=[$963$]b(1-r/a) dr
и момент инерции
dJ=r2dm=[$963$]b(r2-r3/a) dr
Интегрируем
J=0a[$8747$][$963$]b(r2-r3/a) dr=[$963$]b(a3/3-a4/4a)=[$963$]ba3/12
Но масса треугольника
m=[$963$]ab/2
откуда
J= ma2/6=6кг[$183$](0,6м)2/6=0,36 кг[$183$]м2
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