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Консультация № 173412

19.10.2009, 03:48

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Образование

На закрепленную горизонтальную поверхность положили однородный диск радиуса R=20 см, раскрученный предварительно до угловой скорости w=10 рад/с. Определить время t вращения диска на поверхности, если коэффициент трения диска о поверхность равен 0,10

Желательно с разъяснениями действий, заранее спасибо!

Обсуждение

Неизвестный

20.10.2009, 15:22

общий

В начальный момент времени угловая скорость [$969$](0) = [$969$];
В момент остановки t угловая скорость [$969$](t) = 0;
[$969$](t) = [$969$](0) - e*t;
e - угловое ускорение;
Отсюда t = [$969$]/e;

Для момента силы трения имеем: M_тр = I*e;
I = m*R²/2 - момент инерции однородного диска массы m относительно оси вращения;
Тогда t = [$969$]*I/M_тр;

Осталось найти момент силы трения относительно оси вращения.
Сила трения беск.малого участка диска о поверхность dF_тр = [$956$]*dm*g ([$956$] - коэффициент трения);
dm = m*ds/S = m*r*dr*d[$966$]/(pi*R²);
M_тр = [$8747$]dF_тр*r = m*[$956$]*g/(pi*R²)*[$8747$]d[$966$][$8747$]r*r*dr (пределы интегрирования: от 0 до 2*pi и от 0 до R соответственно);

Окончательно
M_тр = (2/3)*[$956$]*m*g*R;
t = [$969$]*I/M_тр = (3/4)*[$969$]*R/([$956$]*g);
t = 1.5 сек.

Форма ответа

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