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Консультация № 177379
20.03.2010, 21:01
0.00 руб.
0
2
1
Уважаемые эксперты, помогите решить задачу, я совсем запутался в ней 
:
Найти момент инерции относительно начала координат однородной плоской фигуры, ограниченной линиями х=2у, х=2, у=0.
:Найти момент инерции относительно начала координат однородной плоской фигуры, ограниченной линиями х=2у, х=2, у=0.
Обсуждение
20.03.2010, 21:51
общий
Фурсик Сергей Вячеславович:
Нет момента инерции относительно точки. Есть момент инерции относительно оси.
Нет момента инерции относительно точки. Есть момент инерции относительно оси.
Неизвестный
21.03.2010, 02:06
общий
это ответ
Здравствуйте, Фурсик Сергей Вячеславович.
Момент инерции относительно начала координат для плоской фигуры D:
Io=[$8747$][$8747$]D p(x,y)*(x2+y2)dxdy
0 [$8804$] x [$8804$] 2 , 0 [$8804$] y [$8804$] x/2
Т.к. фигура однородная, то плотность p(x,y)=P - постоянная , получится
Io=[$8747$][$8747$]D P*(x2+y2)dxdy=P*[$8747$]02dx[$8747$]0x/2(x2+y2)dy=P*[$8747$]02dx(x2*y+y3/3)0x/2=
P*[$8747$]02(x3/2+x3/24)dx=(13/24)*P*[$8747$]02x3dx=(13/24)*P*(x4/4)02=(13/24)*P*(16/4)=(13/6)*P
Ответ: Io=(13/6)*P, где P- постоянная плотности
Момент инерции относительно начала координат для плоской фигуры D:
Io=[$8747$][$8747$]D p(x,y)*(x2+y2)dxdy
0 [$8804$] x [$8804$] 2 , 0 [$8804$] y [$8804$] x/2
Т.к. фигура однородная, то плотность p(x,y)=P - постоянная , получится
Io=[$8747$][$8747$]D P*(x2+y2)dxdy=P*[$8747$]02dx[$8747$]0x/2(x2+y2)dy=P*[$8747$]02dx(x2*y+y3/3)0x/2=
P*[$8747$]02(x3/2+x3/24)dx=(13/24)*P*[$8747$]02x3dx=(13/24)*P*(x4/4)02=(13/24)*P*(16/4)=(13/6)*P
Ответ: Io=(13/6)*P, где P- постоянная плотности
5
Спасибо, Вы очень помогли, а p =1 ;)
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