{"id":46382,"date":"2013-10-18T08:13:33","date_gmt":"2013-10-18T00:13:33","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=46382"},"modified":"2021-10-06T16:20:02","modified_gmt":"2021-10-06T08:20:02","slug":"%e9%9d%9e%e6%85%a3%e6%80%a7%e5%ba%a7%e6%a8%99%e7%b3%bbnon-inertial-reference-frame","status":"publish","type":"post","link":"http:\/\/localhost\/%e9%9d%9e%e6%85%a3%e6%80%a7%e5%ba%a7%e6%a8%99%e7%b3%bbnon-inertial-reference-frame\/","title":{"rendered":"\u975e\u6163\u6027\u5ea7\u6a19\u7cfb (Non-Inertial Reference Frame)"},"content":{"rendered":"

\u975e\u6163\u6027\u5ea7\u6a19\u7cfb (Non-Inertial Reference Frame)<\/strong><\/span>
\n\u570b\u7acb\u81fa\u7063\u5927\u5b78\u7269\u7406\u6240\u9ec3\u4e00\u7384<\/strong><\/span><\/p>\n

\u82e5\u67d0\u4e00\u5ea7\u6a19\u7cfb\u76f8\u5c0d\u65bc\u4efb\u4e00\u6163\u6027\u5ea7\u6a19\u7cfb\u6709\u52a0\u901f\u5ea6\uff0c\u5247\u8a72\u5ea7\u6a19\u7cfb\u7a31\u4e4b\u70ba\u975e\u6163\u6027\u5ea7\u6a19\u7cfb\u3002\u5728\u975e\u6163\u6027\u5ea7\u6a19\u7cfb\u4e2d\uff0c\u7269\u7406\u5b9a\u5f8b\u4e26\u975e\u8655\u5728\u6700\u7c21\u55ae\u5f62\u5f0f\uff0c\u7279\u6b8a\u5730\uff0c\u5c0d\u65bc\u4e00\u500b\u8cea\u91cf\u70ba \u3001\u53d7\u5230\u5916\u529b\u70ba $$F$$\u00a0\u7684\u8cea\u9ede\u4f86\u8aaa\uff0c\u725b\u9813\u5b9a\u5f8b\u4e0d\u518d\u80fd\u55ae\u7d14\u5730\u5beb\u6210 $$F=ma’$$\u00a0\u7684\u5f62\u5f0f(\u5176\u4e2d $$a’$$ \u662f\u975e\u6163\u6027\u5ea7\u6a19\u7cfb\u7684\u89c0\u5bdf\u8005\u6240\u6e2c\u5230\u8cea\u9ede\u7684\u52a0\u901f\u5ea6)\u3002\u70ba\u4e86\u65b9\u4fbf\u63cf\u8ff0\u7269\u9ad4\u7684\u904b\u52d5\uff0c\u4eba\u5011\u9042\u5f15\u5165\u5047\u60f3\u529b\u7684\u6982\u5ff5\uff0c\u4ee4\u00a0F+F\u5047\u60f3\u529b\u00a0<\/sub>=ma’<\/em>\u00a0 \uff0c\u4f7f\u725b\u9813\u5b9a\u5f8b\u7684\u5f62\u5f0f\u5f97\u4ee5\u6210\u7acb\u3002<\/p>\n

\u96d6\u7136\u6211\u5011\u6c38\u9060\u53ef\u4ee5\u9078\u64c7\u53ea\u63a1\u7528\u6163\u6027\u5ea7\u6a19\u7cfb\u4f86\u63cf\u8ff0\u7269\u9ad4\u7684\u904b\u52d5\uff0c\u7136\u800c\u9019\u4e26\u4e0d\u7e3d\u662f\u8655\u7406\u554f\u984c\u6700\u5408\u9069\u7684\u65b9\u5f0f\u3002\u4f8b\u5982\u6211\u5011\u5982\u679c\u60f3\u4e86\u89e3\u53d7\u58d3\u529b\u68af\u5ea6\u5f71\u97ff\u4e0b\u7684\u5927\u6c23\u79fb\u52d5\uff0c\u5247\u56e0\u70ba\u6211\u5011\u662f\u8ddf\u8457\u5730\u7403\u5728\u81ea\u8f49\uff0c\u70ba\u4e86\u80fd\u975e\u5e38\u76f4\u63a5\u800c\u65b9\u4fbf\u5730\u61c9\u7528\u5230\u65e5\u5e38\u751f\u6d3b\u4e2d\uff0c\u6211\u5011\u6703\u9078\u64c7\u5c07\u8a08\u7b97\u7684\u7d50\u679c\u4ee5\u96a8\u8457\u5730\u7403\u81ea\u8f49\u7684\u9019\u500b\u975e\u6163\u6027\u5ea7\u6a19\u7cfb\u4f86\u8868\u793a\u3002<\/p>\n

\u5728\u7dda\u6027\u52a0\u901f\u5ea7\u6a19\u7cfb\u4e2d\uff1a<\/p>\n

\u67d0\u4e00\u5ea7\u6a19\u7cfb $$S’$$ \u4ee5\u5b9a\u52a0\u901f\u5ea6 $$a_0$$\u00a0\u76f8\u5c0d\u65bc\u53e6\u4e00\u6163\u6027\u5ea7\u6a19\u7cfb $$S$$ \u79fb\u52d5\uff0c\u5c0d\u65bc\u4e00\u8655\u5728 $$S$$ \u5ea7\u6a19\u7cfb\u4e0b\u7684\u89c0\u6e2c\u8005\u800c\u8a00\uff0c\u4ed6\u89c0\u6e2c\u5230\u7269\u9ad4\u53d7\u529b\u8207\u52a0\u901f\u5ea6\u7684\u95dc\u4fc2\u662f\uff1a$$F=ma$$\uff0c\u800c\u5c0d\u65bc\u5728 $$S’$$ \u5ea7\u6a19\u7cfb\u4e0b\u7684\u89c0\u6e2c\u8005\u800c\u8a00\uff0c\u529b\u8207\u52a0\u901f\u5ea6\u7684\u95dc\u4fc2\u5247\u662f\uff1a$$F-ma_0=ma’$$\u3002\u9019\u88e1\u5c0d $$S’$$ \u89c0\u6e2c\u8005\u800c\u8a00\uff0c\u5192\u51fa\u4f86\u7684 $$-ma_0$$\u00a0\u5c31\u88ab\u8a6e\u91cb\u70ba\u662f\u5047\u60f3\u529b\u3002<\/p>\n

\u5728\u65cb\u8f49\u5ea7\u6a19\u7cfb\u4e2d\uff1a<\/p>\n

\u5982\u5716\u4e00\u6240\u793a\uff0c\u5047\u8a2d\u4e00\u7269\u9ad4\u653e\u5728\u5713\u76e4\u4e0a\uff0c\u800c\u5713\u76e4\u7e5e\u5176\u4e2d\u5fc3\u4ee5\u5b9a\u89d2\u901f\u5ea6 $$\\omega$$ \u65cb\u8f49\uff0c\u5713\u76e4\u4e0a\u7684\u7269\u9ad4\u8ddd\u96e2\u5713\u76e4\u4e2d\u5fc3\u7684\u8ddd\u96e2\u70ba $$r$$\uff0c\u4e14\u7269\u9ad4\u8207\u5713\u76e4\u4e00\u8d77\u8f49\u52d5(\u7121\u6ed1\u52d5)\u3002\u6b64\u6642\u5c0d\u5728\u5176\u65c1\u908a\u7684\u5730\u9762\u89c0\u6e2c\u8005\u800c\u8a00\uff0c\u7269\u9ad4\u6709 $$\\omega^2r$$ \u7684\u5411\u5fc3\u52a0\u901f\u5ea6\uff0c\u6b32\u7dad\u6301\u6b64\u904b\u52d5\u5c31\u9700\u8981\u4e00\u500b\u5916\u529b $$F$$\uff0c\u6b64\u529b\u5247\u7531\u5713\u76e4\u5c0d\u7269\u9ad4\u7684\u6469\u64e6\u529b\u6216\u56fa\u5b9a\u5668\u4f86\u63d0\u4f9b\u3002\u4f46\u5c0d\u65bc\u8ddf\u96a8\u5713\u76e4\u4e00\u8d77\u65cb\u8f49\u7684\u89c0\u6e2c\u8005\u800c\u8a00\uff0c\u5713\u76e4\u8207\u7269\u9ad4\u90fd\u6c92\u6709\u52d5\uff0c\u800c\u7269\u9ad4\u660e\u660e\u53d7\u5230\u671d\u5167\u7684\u529b $$F$$\u00a0\u4e4b\u4f5c\u7528\u537b\u4ecd\u7dad\u6301\u4e0d\u52d5\uff0c\u6240\u4ee5\u4ed6\u5c31\u5047\u8a2d\u7269\u9ad4\u9084\u53d7\u5230\u67d0\u500b\u770b\u4e0d\u898b\u7684\u529b\u4f86\u5c07\u7269\u9ad4\u671d\u5916\u63a8\uff0c\u9019\u500b\u795e\u79d8\u770b\u4e0d\u898b\u7684\u529b\uff0c\u5c31\u662f\u96e2\u5fc3\u529b(centrifugal force)\u3002<\/p>\n

\"001\"<\/a>

\u5716\u4e00 (\u9673\u7fa9\u88d5\u7e6a)<\/p><\/div>\n

\u5047\u8a2d\u73fe\u5728\u5f9e\u4e0a\u9762\u5713\u76e4\u7684\u4e2d\u5fc3\uff0c\u5411\u5916\u6cbf\u8457\u67d0\u534a\u5f91\u65b9\u5411\u9ad8\u901f\u5c04\u51fa\u4e00\u9846\u7403\uff0c\u4f7f\u7403\u5e7e\u4e4e\u8cbc\u8457\u5713\u76e4\u8868\u9762\u4f4e\u7a7a\u98db\u904e(\u5716\u4e8ca\u53cab)\u5c0d\u5728\u5730\u9762\u7684\u7d05\u8272\u89c0\u6e2c\u8005\u800c\u8a00\uff0c\u7403\u81ea\u96e2\u958b\u4e2d\u5fc3\u9ede\u5f80\u5916\u7de3\u8d70\uff0c\u5168\u7a0b\u90fd\u662f\u8d70\u76f4\u7dda$$(A\\rightarrow B\\rightarrow C\\rightarrow D)$$\uff0c\u53ef\u662f\u7576\u5b83\u5f80\u5916\u7de3\u8d70\u7684\u6642\u5019\uff0c\u6574\u500b\u5713\u76e4\u4e4b\u5916\u7de3\u6703\u4e0d\u65b7\u5f80\u524d\uff0c\u56e0\u6b64\u7403\u76f8\u5c0d\u65bc\u548c\u5713\u76e4\u4e00\u8d77\u65cb\u8f49\u7684\u85cd\u8272\u89c0\u5bdf\u8005\u4f86\u8aaa\u5c31\u843d\u5f8c\u4e86\u4e00\u6b65\u3002\u6545\u5c0d\u65bc\u85cd\u8272\u89c0\u5bdf\u8005\u4f86\u8aaa\uff0c\u7403\u7684\u8ecc\u8de1\u6703\u504f\u79fb\u6210\u4e00\u689d\u5f27\u7dda(\u504f\u79fb\u8ecc\u8de1\u70ba $$A’\\rightarrow B’\\rightarrow C’\\rightarrow D’$$)\u3002\u63db\u8a00\u4e4b\uff0c\u5f9e\u5713\u76e4\u4e0a\u7684\u975e\u6163\u6027\u5ea7\u6a19\u7cfb\u89d2\u5ea6\u4f86\u770b\uff0c\u7403\u597d\u50cf\u662f\u53d7\u5230\u67d0\u4e00\u5047\u60f3\u529b\u4f7f\u5176\u4ee5\u4e00\u5f27\u7dda\u504f\u79fb\uff0c\u800c\u9019\u500b\u8207\u5176\u884c\u5f91\u65b9\u5411\u5782\u76f4\u7684\u529b\u7a31\u70ba\u79d1\u6c0f\u529b(Coriolis force)\u3002<\/p>\n

\"002\"<\/a>

\u5716\u4e8c a \u7403\u958b\u59cb\u81ea\u4e2d\u5fc3\u5c04\u51fa (\u9673\u7fa9\u88d5\u7e6a)<\/p><\/div>\n

\"003\"<\/a>

\u5716\u4e8c b \u7403\u62b5\u9054\u5713\u76e4\u908a\u7de3( \u9673\u7fa9\u88d5\u7e6a)<\/p><\/div>\n

\u4e00\u822c\u800c\u8a00\uff0c\u7269\u9ad4\u65bc\u6163\u6027\u5ea7\u6a19\u7cfb\u8207\u65cb\u8f49\u5ea7\u6a19\u7cfb\u4e0b\u53d7\u529b\u72c0\u6cc1\u4e4b\u5dee\u7570\u53ef\u7528\u4e0b\u5f0f\u8868\u793a<\/p>\n[\u8a3b]\uff1a<\/p>\n

$$ma’=F_{S’}$$ (\u7269\u9ad4\u5728 $$S’$$ \u4e2d\u6240\u53d7\u7684\u529b)<\/p>\n

$$~~~~~~=F$$ (\u7269\u9ad4\u5728 $$S$$ \u4e2d\u6240\u53d7\u7684\u771f\u5be6\u529b\u91cf $$=ma$$)<\/p>\n

$$~~~~~~~~~+{-ma_1}$$ ($$S’$$ \u76f8\u5c0d\u65bc $$S$$ \u7684\u7dda\u52a0\u901f\u5ea6\u6240\u7522\u751f\u7684\u5047\u60f3\u529b)<\/p>\n

$$~~~~~~~~~+\\{-m\\vec{\\omega}\\times(\\vec{\\omega}\\times \\vec{r})\\}$$ (\u96e2\u5fc3\u529b) $$+\\{-2m\\vec{\\omega}\\times\\vec{v}\\}$$ (\u79d1\u6c0f\u529b)<\/p>\n

\u6211\u5011\u53ef\u4ee5\u8aaa\u725b\u9813\u5b9a\u5f8b\u5728\u4efb\u4f55\u5ea7\u6a19\u7cfb\u4e0b\u90fd\u6210\u7acb\uff0c\u53ea\u8981\u529b\u88ab\u91cd\u65b0\u5b9a\u7fa9\u6210\u5305\u542b\u5047\u60f3\u529b\u5728\u5167\u3002\u800c\u975e\u6163\u6027\u5ea7\u6a19\u7cfb\u4e5f\u53ef\u5b9a\u7fa9\u6210\uff1a\u9700\u8981\u52a0\u5165\u5047\u60f3\u529b\uff0c\u4f7f\u5f97\u725b\u9813\u7269\u7406\u5b9a\u5f8b\u6210\u7acb\u7684\u5ea7\u6a19\u7cfb\u3002<\/p>\n[\u8a3b]\u63a8\u5c0e\u53ef\u53c3\u8003Ryder, p84-85<\/p>\n

\u53c3\u8003\u8cc7\u6599:<\/strong><\/p>\n

    \n
  1. http:\/\/en.wikipedia.org\/wiki\/Non-inertial_reference_frame<\/li>\n
  2. Lawrence E. Goodman and William H. Warner, Dynamics<\/i>, 3rd<\/sup> ed, p358 Dover Publications (2001),<\/li>\n
  3. Peter Ryder, Classical Mechanics<\/i>, Shaker Verlag GmbH, Germany (2007).<\/li>\n<\/ol>\n<\/div>","protected":false},"excerpt":{"rendered":"

    \u975e\u6163\u6027\u5ea7\u6a19\u7cfb (Non-Inertial Reference Frame) \u570b\u7acb\u81fa\u7063\u5927\u5b78\u7269\u7406\u6240\u9ec3\u4e00\u7384 \u82e5\u67d0\u4e00\u5ea7…<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[107,9,3],"tags":[2231,5568,5571,1172,5572,2004],"class_list":["post-46382","post","type-post","status-publish","format-standard","hentry","category-physics00","category-physics01-06","category-physics01","tag-2231","tag-5568","tag-5571","tag-1172","tag-5572","tag-2004","loop-entry","cat-107","cat-9","cat-3","no-thumbnail"],"views":7233,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/46382","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=46382"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/46382\/revisions"}],"predecessor-version":[{"id":87408,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/46382\/revisions\/87408"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=46382"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=46382"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=46382"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}