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Консультация № 108527
08.11.2007, 07:44
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Уважаемые эксперты, пожалуйста помогите решить задачки. Заранее большое спасибо. C уважение Роман Александрович.
1) Определить момент инерции тонкого стержня длинной 30 см. и массой 100г. Относительно оси, перпендикулярной стержню и проходящей через точку, отстоящую от конца стержня на одну треть его длины.
1) Определить момент инерции тонкого стержня длинной 30 см. и массой 100г. Относительно оси, перпендикулярной стержню и проходящей через точку, отстоящую от конца стержня на одну треть его длины.
Обсуждение
Неизвестный
09.11.2007, 00:22
общий
это ответ
Здравствуйте, Чурнов Роман Александрович!
Момент инерции стержня относительно его конца (1/3)*M*L^2.
Разобьём наш стержень на 2 куска: длины (1/3)*L и массы (1/3)*M и длины (2/3)*L и массы (2/3)*M.
Момент инерции нашего стержня равен сумме моментов инерции этих кусокв
J = (1/3)*(1/3)*M*((1/3)*L)^2 + (1/3)*(2/3)*M*((2/3)*L)^2 = (1/3)*M*L^2*((1/3)^3 + (2/3)^3) = (1/9)*M*L^2
Момент инерции стержня относительно его конца (1/3)*M*L^2.
Разобьём наш стержень на 2 куска: длины (1/3)*L и массы (1/3)*M и длины (2/3)*L и массы (2/3)*M.
Момент инерции нашего стержня равен сумме моментов инерции этих кусокв
J = (1/3)*(1/3)*M*((1/3)*L)^2 + (1/3)*(2/3)*M*((2/3)*L)^2 = (1/3)*M*L^2*((1/3)^3 + (2/3)^3) = (1/9)*M*L^2
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