sol_13_09 - 13 1.1 Z I= r2 dm,r x = 0 x r,adx dx Z 1b 2 2 b...

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ÆØÆ° ±oe oeLØælÆز³° ´Øµ³²³lLæ°³ ´¶ØæØ·± l·æ´ oeØÆ 13 l°æ± ²Ø³loe ´µloe° - 1 oeØ液· ¸·ØæØ° .1 lª¸³µ ´Ø¹l²Ø° L²µ³µ (°) I = r 2 dm oeزƱµ ´æ³l· ø³l·² º° ,»Æ±µ´ l³Æ¼ .oeØø°l´µ ¶½lµ´ °±³ (lع´ ±° ºØ°¹µ² ´Æ ´ª³¶²´µ OE²°´) ƳÆØæ´ lعµ ¶½lµ´ °³´ ,»°º , r lø°º (»Æ±µ´ ¾ºlµÆ x = 0 ) x »°º °³´ lع´µ r ¶½lµ´ .»Æ±µ´ ±ø oeؽLøµ´ (´æµ) oe³·Ø·¹´ °Ø´ σ lø°º , a σ dx °Ø´ ´±ø ´æµ´ dx ØƳ¼Æ oeغ²° ´°lØ ±l¸L²Ø°´ »º±³ I = 1 2 b x = - 1 2 b x 2 a σ dx = 2 3 σ a b 2 3 = 1 12 σ ab 3 , I = 1 12 Mb 2 (.³¾ºlµ ÆØÆæ ¶ª L³µ± ³µº ´½æ³² ´oe³° ¶³ØªÆ ³¾ø Ʊ ³µØø) .»Æ±µ´ oeæµ °Ø´ M σ ab lø°º oe³Øº²° oe³æ³l·± ³° (³±ø ´¹¶´ ÆØÆæ L³µ ±ø I ) 1 3 x 2 dm ´Ø¹l²Ø° L²µ³µ ª½° ±º± lø°º ºØض·³° ºØ¶ª oe³L³µ± ³° ø³l·± lø·° ø±³øµ´ oe° (Æ) °Ø´ loeص´ oe°³³øµ ¾°³ ,(»³oe½oeÆ º¸ lø·°) ø±³øµ´ ±ø »³Ø±¼´ ´¹¶Æ y = 0 oe° l½Æ² .lع´µ ´²³ø x ¶½lµÆ oe½° ±º oe³l¹¶oeµ³ oe³º±³´ø Æع² . dI = 1 3 dmx 2 = 1 3 σ xdyx 2 °³´ dy ØƳ¼Æ ´æ³l· ±º ±ø ´Ø¹l²Ø°´ L²µ³µ (ºØض·³° oe³L³µ) ´²³ø°l´ ´LØøÆ . x = - b a y ³° y = - a b x ±Æ¶²³ ±l¸L²Ø°Æ I = 1 3 σ 0 y = - a x 3 dy = 1 3 σ 0 y = - a - b a y 3 dy = 1 12 σ b 3 a = , I = 1 6 Mb 2 .ø±³øµ´ oeæµ °³´ M 1 2 ab lø°º ( dm = σ ( a - a b x ) dx oe³Øº²° oe³æ³l·) ´Ø²ø´ ´LØøÆ I = b x = 0 x 2 σ ( a - a b x ) dx = σ a 1 3 b 3 - 1 4 b 3 = 1 12 σ b 3 a = 1 6 Mb 2 ´l¶µÆ .lع´ ³oe³° ÆØÆæ ´Ø¹l²Ø° ØL²µ³µ læ½±/lƽ± loe³µ ¾° ,( m i r 2 i ±ø º³ºæµ oeƺl³µ) oeØl°²Ø± °Ø´ ´Ø¹l²Ø°´ L²µ³µ± ´½æ³²´ø »³³Øºµ (¸) °³´ (±¸¼µ´ ¾ºlµ) ³¾ºlµ ÆØÆæ , a æ³Øªl³ m ´æµ ±¼Æ ,±Ø±¸ ±ø ´Ø¹l²Ø°´ L²µ³µ ,»°º . 1 2 ma 2 °³´ 1 2 a ¶½lµÆ OE° ±Øƶµ lع ÆØÆæ , 1 3 a æ³Øªl³ m ´æµ ±¼Æ ±Ø±¸ ±ø ´Ø¹l²Ø°´ L²µ³µ l²ØØLø L·øµ oel¾¼Æ . 1 2 m a 3 2 + m a 2 2 = 11 36 m a 2 °³´ ¿³¸´ ±ø ´Ø¹l²Ø°´ L²µ³µ ¾° ,ºØl³½ ´¼Æl° ³²± øØø »³³Øºµ I = 1 2 ma 2 - 4 11 36 m a 2 3
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:(¼³ÆØlÆ æ³Øªl± Øæ½Ø ½Lø´) °±µ´ ±Ø±¸´ ±ø ³¾µ 1 9 °Ø´ ª½° ±º ±ø ´æµ´ ¾° ±Ø±¸´ ±ø 1 3 °³´ ºØl³½´ æ³Øªlø »³³Øºµ . m = 1 9 m °Ø´ ¿³¸´ oeæµø »°ºµ M = m - 4 · 1 9 m = 5 9 m ³° . m = 9 5 M ±Æ¶²³ ³²°¹µø I -Æ Æع² I = . ( 1 2 - 11 81 ) ma 2 = 59 90 Ma 2 ª½° ±º :¿oe³øµ ¾ºlµ ر¼Æ ºØ¶ª ºØ±³±½ ºØ±Ø±¸ oel¾¼Æ ³° Æø½± lø·° (³¾ºlµÆ lƳ¼´ غ²° lع ÆØÆæ) , R æ³Øªl ±¼Æ l³ªº ±ø ´Ø¹l²Ø°´ L²µ³µ oe° .2
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