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Консультация № 202959
01.06.2022, 21:04
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Здравствуйте! У меня возникли сложности с таким вопросом:
Диск радиуса м начал вращаться вокруг своей оси без начальной скорости с угловым ускорением, зависящим от времени E=A(T/t)^4 . На какой угол (в радианах) он повернется за время T=1 с, если t=1 с? А = 7 *с–2.
Диск радиуса м начал вращаться вокруг своей оси без начальной скорости с угловым ускорением, зависящим от времени E=A(T/t)^4 . На какой угол (в радианах) он повернется за время T=1 с, если t=1 с? А = 7 *с–2.
Обсуждение
01.06.2022, 23:12
общий
Адресаты:
Уточните формулу для углового ускорения: какая из переменных - текущее время, а какая - константа?
01.06.2022, 23:21
общий
это ответ
Здравствуйте, Foxlife!
Предлагаю Вам следующее решение задачи.
Дано: диск начал вращаться вокруг своей оси без начальной скорости, то есть
рад -- угол поворота диска в начальный момент времени 
с; 
рад/с -- угловая скорость диска в начальный момент времени; 
рад/с2 -- зависимость углового ускорения диска от времени 
Определить:
-- угол поворота диска за время 
с.
Интегрируя заданную зависимость, получим, что
Поскольку
рад/с, постольку 
Далее,
Поскольку
рад, постольку 
Следовательно, искомый угол, согласно формуле Ньютона -- Лейбница, составляет
(рад).
Ответ:
рад.
Предлагаю Вам следующее решение задачи.
Дано: диск начал вращаться вокруг своей оси без начальной скорости, то есть
рад -- угол поворота диска в начальный момент времени с; рад/с -- угловая скорость диска в начальный момент времени; рад/с2 -- зависимость углового ускорения диска от времени Определить:
-- угол поворота диска за время с.Решение
Интегрируя заданную зависимость, получим, что
Поскольку
рад/с, постольку Далее,
Поскольку
рад, постольку Следовательно, искомый угол, согласно формуле Ньютона -- Лейбница, составляет (рад).Ответ:
рад.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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