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Консультация № 195391
26.04.2019, 22:38
0.00 руб.
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1
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Диск вращается вокруг оси, проходящей через его центр масс. Зависимость угла поворота от времени имеет вид φ = 4 - 0,4t - 0,02t2 + 0,01t3 (рад). Для момента времени t1=3 с найти: а) угловой путь, пройденный к этому моменту времени, б) угловую скорость, в) угловое ускорение, г) определить для точки, находящейся на расстоянии 0,4 м от оси вращения полное линейное ускорение в момент времени, когда линейная скорость точки 0,46 м/с.
Диск вращается вокруг оси, проходящей через его центр масс. Зависимость угла поворота от времени имеет вид φ = 4 - 0,4t - 0,02t2 + 0,01t3 (рад). Для момента времени t1=3 с найти: а) угловой путь, пройденный к этому моменту времени, б) угловую скорость, в) угловое ускорение, г) определить для точки, находящейся на расстоянии 0,4 м от оси вращения полное линейное ускорение в момент времени, когда линейная скорость точки 0,46 м/с.
Обсуждение
29.04.2019, 10:07
общий
это ответ
Здравствуйте, qazxswedc!
При заданной зависимости
угла поворота диска от времени его угловая скорость 
и угловое ускорение 
составляют соответственно
Поскольку при
с угловая скорость диска отрицательна (смотрите график), постольку угловой путь, пройденный к моменту времени 
с, равен угловому перемещению, то есть
а)
(рад).
При с, согласно формулам (1), (2), получим
б)
(рад/с);
в)
(рад/с2).
В момент времени, когда линейная скорость заданной точки равна
м/с, её угловая скорость составляет
(рад/с).
Тогда, в соответствии с формулой (1),
(с),
то есть заданной скорости указанная точка на диске достигает к моменту времени
с. В этот момент времени её угловая скорость, угловое ускорение и полное линейное ускорение составляют
(рад/с),
(рад/с2),
г)
(м/с2).
Проверьте расчёт во избежание ошибок, если хотите им воспользоваться.
При заданной зависимости
угла поворота диска от времени его угловая скорость и угловое ускорение составляют соответственноПоскольку при
с угловая скорость диска отрицательна (смотрите график), постольку угловой путь, пройденный к моменту времени с, равен угловому перемещению, то естьа)
(рад).При
с, согласно формулам (1), (2), получимб)
(рад/с);в)
(рад/с2).В момент времени, когда линейная скорость заданной точки равна
м/с, её угловая скорость составляет (рад/с).Тогда, в соответствии с формулой (1),
(с),то есть заданной скорости указанная точка на диске достигает к моменту времени
с. В этот момент времени её угловая скорость, угловое ускорение и полное линейное ускорение составляют (рад/с), (рад/с2),г)
(м/с2).Проверьте расчёт во избежание ошибок, если хотите им воспользоваться.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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