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Консультация № 194855
03.03.2019, 14:28
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Найти координаты центра тяжести однородной пластинки, ограниченной линиями, плотность γ принять равной единице (γ=1):
x^2+y^2=4 , x⩾0, у⩾0
Найти координаты центра тяжести однородной пластинки, ограниченной линиями, плотность γ принять равной единице (γ=1):
x^2+y^2=4 , x⩾0, у⩾0
Обсуждение
04.03.2019, 10:00
общий
это ответ
Здравствуйте, Helen!
Заданная однородная пластинка представляет собой четверть круга, имеющего радиус
ед. длины. Ось симметрии этой пластинки совпадает с биссектрисой прямого угла. Значит, если принять вершину прямого угла за начало полярной системы координат, а полярный угол отсчитывать от одного прямолинейного края пластинки к другому, то полярный угол центра тяжести пластинки составляет 
Чтобы вычислить полярный радиус центра тяжести пластинки, воспользуемся указанием на с. 327 (в доступном для чтения на компьютере формате это с. 328 (здесь). По формуле (III.69a) получим
Значит, в полярной системе координат, введённой так, как указано выше, полярные координаты центра тяжести пластинки суть
В декартовой прямоугольной системе координат, начало которой совпадает с началом полярной системы координат, а оси абсцисс и ординат направлены вдоль прямолинейных краёв пластинки так, что пластинка опирается на их положительные полуоси, координаты центра тяжести пластинки суть
Заданная однородная пластинка представляет собой четверть круга, имеющего радиус
ед. длины. Ось симметрии этой пластинки совпадает с биссектрисой прямого угла. Значит, если принять вершину прямого угла за начало полярной системы координат, а полярный угол отсчитывать от одного прямолинейного края пластинки к другому, то полярный угол центра тяжести пластинки составляет Чтобы вычислить полярный радиус центра тяжести пластинки, воспользуемся указанием на с. 327 (в доступном для чтения на компьютере формате это с. 328 (здесь). По формуле (III.69a) получимЗначит, в полярной системе координат, введённой так, как указано выше, полярные координаты центра тяжести пластинки суть
В декартовой прямоугольной системе координат, начало которой совпадает с началом полярной системы координат, а оси абсцисс и ординат направлены вдоль прямолинейных краёв пластинки так, что пластинка опирается на их положительные полуоси, координаты центра тяжести пластинки суть
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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