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{"id":28782,"date":"2018-04-27T16:14:10","date_gmt":"2018-04-27T09:14:10","guid":{"rendered":"https:\/\/lop12.edu.vn\/?p=28782"},"modified":"2018-04-27T16:14:10","modified_gmt":"2018-04-27T09:14:10","slug":"bai-tap-trac-nghiem-hinh-hoc-12-chuong-2-bai-1-khai-niem-ve-mat-tron-xoay","status":"publish","type":"post","link":"https:\/\/lop12.edu.vn\/bai-tap-trac-nghiem-hinh-hoc-12-chuong-2-bai-1-khai-niem-ve-mat-tron-xoay\/","title":{"rendered":"B\u00e0i t\u1eadp tr\u1eafc nghi\u1ec7m H\u00ecnh h\u1ecdc 12 \u2013 Ch\u01b0\u01a1ng 2 – B\u00e0i 1: Kh\u00e1i ni\u1ec7m v\u1ec1 m\u1eb7t tr\u00f2n xoay"},"content":{"rendered":"

1. S\u1ef1 t\u1ea1o th\u00e0nh m\u1eb7t tr\u00f2n xoay<\/b><\/p>\n

Trong kh\u00f4ng gian cho m\u1eb7t ph\u1eb3ng (P) ch\u1ee9a \u0111\u01b0\u1eddng th\u1eb3ng \u0394 v\u00e0 ch\u1ee9 \u0111\u01b0\u1eddng L. Khi quay m\u1eb7t (P) xung quanh \u0394 m\u1ed9t g\u00f3c 360o<\/sup>\u00a0th\u00ec \u0111\u01b0\u1eddng L t\u1ea1o n\u00ean m\u1ed9t m\u1eb7t tr\u00f2n xoay. M\u1eb7t tr\u00f2n xoay \u0111\u00f3 nh\u1eadn \u0394 l\u00e0m tr\u1ee5c, \u0111\u01b0\u1eddng L \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u01b0\u1eddng sinh.<\/p>\n

2. T\u00ednh ch\u1ea5t c\u1ee7a m\u1eb7t tr\u00f2n xoay<\/b><\/p>\n

– N\u1ebfu c\u1eaft m\u1eb7t tr\u00f2n xoay b\u1edfi m\u1ed9t m\u1eb7t ph\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi tr\u1ee5c \u0394 ta \u0111\u01b0\u1ee3c ph\u1ea7n giao l\u00e0 \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 t\u00e2m thu\u1ed9c tr\u1ee5c \u0394<\/p>\n

– M\u1ed7i \u0111i\u1ec3m M tr\u00ean m\u1eb7t tr\u00f2n xoay \u0111\u1ec1u n\u1eb1m tr\u00ean m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n thu\u1ed9c m\u1eb7t tr\u00f2n xoay v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n n\u00e0y c\u00f3 t\u00e2m thu\u1ed9c tr\u1ee5c \u0394<\/p>\n

3. M\u1eb7t n\u00f3n tr\u00f2n xoay.<\/b><\/p>\n

1. \u0110\u1ecbnh ngh\u0129a.<\/b><\/p>\n

Trong m\u1eb7t ph\u1eb3ng (P) cho hai \u0111\u01b0\u1eddng th\u1eb3ng \u0394 v\u00e0 d c\u1eaft nhau t\u1ea1i \u0111i\u1ec3m O v\u00e0 t\u1ea1o v\u1edbi nhau m\u1ed9t g\u00f3c \u03b1 v\u1edbi 0o<\/sup>\u00a0< \u03b1 < 90o<\/sup>. M\u1eb7t tr\u00f2n xoay sinh ra b\u1edfi \u0111\u01b0\u1eddng th\u1eb3ng d khi quay m\u1eb7t ph\u1eb3ng (P) xung quanh \u0394 g\u1ecdi l\u00e0 m\u1eb7t n\u00f3n tr\u00f2n xoay \u0111\u1ec9nh O (\u0111\u01b0\u1ee3c g\u1ecdi t\u1eaft l\u00e0 m\u1eb7t n\u00f3n). \u0110\u01b0\u1eddng th\u1eb3ng \u0394 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 tr\u1ee5c, \u0111\u01b0\u1eddng th\u1eb3ng d \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u01b0\u1eddng sinh, g\u00f3c 2\u03b1 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 g\u00f3c \u1edf \u0111\u1ec9nh c\u1ee7a m\u1eb7t n\u00f3n tr\u00f2n xoay.<\/p>\n

2. T\u00ednh ch\u1ea5t<\/b><\/p>\n

a) N\u1ebfu c\u1eaft m\u1eb7t n\u00f3n tr\u00f2n xoay \u0111\u1ec9nh O b\u1edfi m\u1eb7t ph\u1eb3ng \u0111i qua \u0111\u1ec9nh O ta c\u00f3 c\u00e1c tr\u01b0\u1eddng h\u1ee3p sau \u0111\u00e2y:<\/p>\n

– M\u1eb7t ph\u1eb3ng c\u1eaft m\u1eb7t n\u00f3n theo hai \u0111\u01b0\u1eddng sinh<\/p>\n

– M\u1eb7t ph\u1eb3ng ti\u1ebfp x\u00fac v\u1edbi m\u1eb7t n\u00f3n theo m\u1ed9t \u0111\u01b0\u1eddng sinh. Trong tr\u01b0\u1eddng h\u1ee3p n\u00e0y ng\u01b0\u1eddi ta th\u01b0\u1eddng g\u1ecdi m\u1eb7t ph\u1eb3ng \u0111\u00f3 l\u00e0 ti\u1ebfp di\u1ec7n c\u1ee7a m\u1eb7t n\u00f3n.<\/p>\n

– M\u1eb7t ph\u1eb3ng ch\u1ec9 c\u00f3 \u0111i\u1ec3m O chung duy nh\u1ea5t v\u1edbi m\u1eb7t n\u00f3n, ngo\u00e0i ra kh\u00f4ng c\u00f3 \u0111i\u1ec3m chung n\u00e0o kh\u00e1c.<\/p>\n

b) N\u1ebfu c\u1eaft m\u1eb7t n\u00f3n tr\u00f2n xoay \u0111\u1ec9nh O b\u1edfi m\u1eb7t ph\u1eb3ng (P) kh\u00f4ng \u0111i qua \u0111\u1ec9nh o ta c\u00f3 nh\u1eefng tr\u01b0\u1eddng h\u1ee3p sau:<\/p>\n

– N\u1ebfu m\u1eb7t ph\u1eb3ng (P) c\u1eaft m\u1ecdi \u0111\u01b0\u1eddng sinh c\u1ee7a m\u1eb7t n\u00f3n, ta \u0111\u01b0\u1ee3c ph\u00e0n giao l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng elip ho\u1eb7c m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n (khi m\u1eb7t ph\u1eb3ng (P) vu\u00f4ng g\u00f3c v\u1edbi tr\u1ee5c \u0394 c\u1ee7a m\u1eb7t n\u00f3n)<\/p>\n

– N\u1ebfu m\u1eb7t ph\u1eb3ng (P) song song v\u1edbi ch\u1ec9 m\u1ed9t \u0111\u01b0\u1eddng sinh c\u1ee7a m\u1eb7t n\u00f3n ta \u0111\u01b0\u1ee3c ph\u1ea7n giao ch\u00ednh l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng parabol<\/p>\n

– N\u1ebfu m\u1eb7t ph\u1eb3ng (P) song song v\u1edbi 2 \u0111\u01b0\u1eddng sinh c\u1ee7a m\u1eb7t n\u00f3n ta \u0111\u01b0\u1ee3c ph\u1ea7n giao l\u00e0 hai nh\u00e1nh c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng hypebol<\/p>\n

3. H\u00ecnh n\u00f3n tr\u00f2n xoay v\u00e0 kh\u1ed1i n\u00f3n tr\u00f2n xoay<\/b><\/p>\n

Cho tam gi\u00e1c OIM vu\u00f4ng t\u1ea1i I. Khi quay tam gi\u00e1c \u0111\u00f3 xung quanh c\u1ea1nh g\u00f3c vu\u00f4ng OI th\u00ec \u0111\u01b0\u1eddng g\u1ea5p kh\u00fac OMI t\u1ea1o th\u00e0nh m\u1ed9t h\u00ecnh \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 h\u00ecnh n\u00f3n tr\u00f2n xoay (hay \u0111\u01b0\u1ee3c g\u1ecdi t\u1eaft l\u00e0 h\u00ecnh n\u00f3n). H\u00ecnh tr\u00f2n t\u00e2m I b\u00e1n k\u00ednh IM \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 m\u1eb7t \u0111\u00e1y, \u0111i\u1ec3m O \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u1ec9nh, \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n OI g\u1ecdi l\u00e0 chi\u1ec1u cao v\u00e0 \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n OM \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng sinh c\u1ee7a h\u00ecnh n\u00f3n \u0111\u00f3.<\/p>\n

4. Di\u1ec7n t\u00edch xung quanh v\u00e0 di\u1ec7n t\u00edch to\u00e1n ph\u1ea7n c\u1ee7a h\u00ecnh n\u00f3n tr\u00f2n xoay.<\/b><\/p>\n

– G\u1ecdi Sxq<\/sub>\u00a0l\u00e0 di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh n\u00f3n c\u00f3 b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00e1y b\u1eb1ng r v\u00e0 c\u00f3 \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng sinh b\u1eb1ng l . Khi \u0111\u00f3 ta c\u00f3 c\u00f4ng th\u1ee9c: Sxq<\/sub>\u00a0= \u03c0rl<\/p>\n

– Di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh n\u00f3n l\u00e0 t\u1ed5ng di\u1ec7n t\u00edch xung quanh v\u00e0 di\u1ec7n t\u00edch \u0111\u00e1y. G\u1ecdi Stp<\/sub>\u00a0l\u00e0 di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh n\u00f3n. Ta c\u00f3 c\u00f4ng th\u1ee9c: Stp<\/sub>\u00a0= \u03c0r(r + l)<\/p>\n

5. Th\u1ec3 t\u00edch kh\u1ed1i n\u00f3n tr\u00f2n xoay<\/b><\/p>\n

G\u1ecdi V l\u00e0 th\u1ec3 t\u00edch kh\u1ed1i n\u00f3n tr\u00f2n xoay c\u00f3 chi\u1ec1u cao h v\u00e0 c\u00f3 b\u00e1n k\u00ednh \u0111\u00e1y r. Khi \u0111\u00f3 ta c\u00f3 c\u00f4ng th\u1ee9c:<\/p>\n

\"\"<\/p>\n","protected":false},"excerpt":{"rendered":"

1. S\u1ef1 t\u1ea1o th\u00e0nh m\u1eb7t tr\u00f2n xoay Trong kh\u00f4ng gian cho m\u1eb7t ph\u1eb3ng (P) ch\u1ee9a \u0111\u01b0\u1eddng th\u1eb3ng \u0394 v\u00e0 ch\u1ee9 \u0111\u01b0\u1eddng L. Khi quay m\u1eb7t (P) xung quanh \u0394 m\u1ed9t g\u00f3c 360o\u00a0th\u00ec \u0111\u01b0\u1eddng L t\u1ea1o n\u00ean m\u1ed9t m\u1eb7t tr\u00f2n xoay. M\u1eb7t tr\u00f2n xoay \u0111\u00f3 nh\u1eadn \u0394 l\u00e0m tr\u1ee5c, \u0111\u01b0\u1eddng L \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u01b0\u1eddng sinh. […]<\/p>\n","protected":false},"author":3,"featured_media":28783,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[157],"tags":[1450,1448],"yoast_head":"\nB\u00e0i t\u1eadp tr\u1eafc nghi\u1ec7m H\u00ecnh h\u1ecdc 12 \u2013 Ch\u01b0\u01a1ng 2 - B\u00e0i 1: Kh\u00e1i ni\u1ec7m v\u1ec1 m\u1eb7t tr\u00f2n xoay<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/lop12.edu.vn\/bai-tap-trac-nghiem-hinh-hoc-12-chuong-2-bai-1-khai-niem-ve-mat-tron-xoay\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"B\u00e0i t\u1eadp tr\u1eafc nghi\u1ec7m H\u00ecnh h\u1ecdc 12 \u2013 Ch\u01b0\u01a1ng 2 - B\u00e0i 1: Kh\u00e1i ni\u1ec7m v\u1ec1 m\u1eb7t tr\u00f2n xoay\" \/>\n<meta property=\"og:description\" content=\"1. S\u1ef1 t\u1ea1o th\u00e0nh m\u1eb7t tr\u00f2n xoay Trong kh\u00f4ng gian cho m\u1eb7t ph\u1eb3ng (P) ch\u1ee9a \u0111\u01b0\u1eddng th\u1eb3ng \u0394 v\u00e0 ch\u1ee9 \u0111\u01b0\u1eddng L. Khi quay m\u1eb7t (P) xung quanh \u0394 m\u1ed9t g\u00f3c 360o\u00a0th\u00ec \u0111\u01b0\u1eddng L t\u1ea1o n\u00ean m\u1ed9t m\u1eb7t tr\u00f2n xoay. M\u1eb7t tr\u00f2n xoay \u0111\u00f3 nh\u1eadn \u0394 l\u00e0m tr\u1ee5c, \u0111\u01b0\u1eddng L \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u01b0\u1eddng sinh. 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S\u1ef1 t\u1ea1o th\u00e0nh m\u1eb7t tr\u00f2n xoay Trong kh\u00f4ng gian cho m\u1eb7t ph\u1eb3ng (P) ch\u1ee9a \u0111\u01b0\u1eddng th\u1eb3ng \u0394 v\u00e0 ch\u1ee9 \u0111\u01b0\u1eddng L. Khi quay m\u1eb7t (P) xung quanh \u0394 m\u1ed9t g\u00f3c 360o\u00a0th\u00ec \u0111\u01b0\u1eddng L t\u1ea1o n\u00ean m\u1ed9t m\u1eb7t tr\u00f2n xoay. M\u1eb7t tr\u00f2n xoay \u0111\u00f3 nh\u1eadn \u0394 l\u00e0m tr\u1ee5c, \u0111\u01b0\u1eddng L \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u01b0\u1eddng sinh. 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