![\"\"](\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/anvvr.jpg\")
<\/center>\n\u4e0a\u56fe\u662f2011\u5e74\u6768\u632f\u5b81\u5148\u751f\u5728\u9999\u6e2f\u6d78\u4f1a\u5927\u5b66\u6f14\u8bb2[?<\/a>]PPT\u7684\u4e00\u5f20\u622a\u56fe\uff0c\u5e74\u8fd1\u4e5d\u5341\u7684\u4ed6\u8fd8\u8bb0\u5f97\u4e03\u5341\u591a\u5e74\u524d\u81ea\u5b66\u5230\u5411\u5fc3\u52a0\u901f\u5ea6\u7684\u4e8b\u60c5\uff0c\u4f5c\u4e3a\u6559\u5e08\u6df1\u77e5\u5bf9\u52a0\u901f\u5ea6\u7684\u76f4\u89c9\u548c\u5411\u5fc3\u52a0\u901f\u5ea6\u5411\u91cf\u8fd0\u7b97\u7ed3\u679c\u7684\u51b2\u7a81\u662f\u4e00\u4e2a\u666e\u904d\u7684\u8ba4\u77e5\u73b0\u8c61\uff0c\u6b63\u5982\u6768\u5148\u751f\u63d0\u5230\u7684\u90a3\u6837\uff0c\u5bf9\u5411\u5fc3\u52a0\u901f\u5ea6\u6c42\u89e3\u7684\u7406\u89e3\u4e5f\u662f\u5f88\u597d\u7684\u63d0\u5347\u673a\u4f1a\u3002
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![\"\"](\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/awvr1.png\")
<\/center>\n\u2460<\/strong>\u91cd\u65b0\u601d\u8003\u8fd9\u4e2a\u95ee\u9898\uff08deriving formula for centripetal acceleration\uff09\u4e5f\u662f\u53d7\u80e1\u8317\u6dde\u540c\u5b66\u5206\u4eab\u7684\u4e00\u79cd\u65cb\u8f6c\u7c7b\u6bd4\u65b9\u6cd5\u7684\u542f\u53d1\uff0c\u4ee5\u5300\u901f\u8f6c\u52a8\u7269\u4f53\u4e3a\u53c2\u8003\u70b9\u8fdb\u884c\u5411\u91cf\u5e73\u79fb\uff0c\u5411\u5fc3\u52a0\u901f\u5ea6a\u3001\u89d2\u901f\u5ea6$$\\omega$$\u548c\u7ebf\u901f\u5ea6v\u5206\u522b\u548c\u7b49\u901f\u5706\u5468\u8fd0\u52a8\u7684\u7ebf\u901f\u5ea6v\u3001\u89d2\u901f\u5ea6$$\\omega$$\u548c\u534a\u5f84r\u5bf9\u5e94\uff0c$$v=\\frac{\\Delta r}{\\Delta t}$$\uff0c$$a=\\frac{\\Delta v}{\\Delta t}$$\uff0c\u65e2\u7136$$v=\\omega r$$\uff0c\u90a3$$a=\\omega v$$\u3002\uff08$$\\vec{a}=\\vec{\\omega}\\times\\vec{v}$$\u662f$$\\vec{v}=\\vec{\\omega}\\times\\vec{r}$$\u5173\u4e8e\u65f6\u95f4\u7684\u6c42\u5bfc…\uff09
\n\u5173\u4e8e\u89d2\u901f\u5ea6\u7684\u77e2\u91cf\u65b9\u5411\uff0c\u6ee1\u8db3\u53f3\u624b\u87ba\u65cb\u5b9a\u5219\uff0c\u5927\u62c7\u6307\u65b9\u5411\u4e3a\u03c9\u65b9\u5411\uff0c\u800c\u7ebf\u901f\u5ea6\u548c\u5411\u5fc3\u52a0\u901f\u5ea6\u7c7b\u6bd4\u7535\u78c1\u611f\u5e94\u90e8\u5206\u7684\u624b\u5219…<\/em>
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![\"\"](\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/awvr2.png\")
<\/center>\n\u6211\u63a5\u89e6\u7684\u6700\u5e38\u89c1\u7684\u65b9\u6cd5\u662f\u77e2\u91cf\u4e09\u89d2\u5f62\u548c\u51e0\u4f55\u4e09\u89d2\u5f62\u76f8\u4f3c\uff1a
\n\u2461<\/strong>\u8fd9\u79bb\u4e0d\u5f00\u7528\u5f27\u957f\u8fd1\u4f3c\u5f26\u957f\u3002$$\\Delta l\\approx \\Delta s =v \\Delta t$$\uff0c$$\\frac{\\Delta v}{\\Delta s}=\\frac{v}{r}$$\uff0c$$\\frac{\\Delta v}{v\\Delta t}=\\frac{v}{r}$$\uff0c$$a=\\frac{\\Delta v}{\\Delta t}=\\frac{v^2}{r}$$\uff1b
\n\u2462<\/strong>\u6216\u8005\u7528\u5f27\u957f$$\\Delta s =r\\Delta\\theta=r\\omega\\Delta t$$\u8fd1\u4f3c\u5f26\u957f\uff0c$$\\frac{\\Delta v}{r\\omega\\Delta t}=\\frac{v}{r}$$\uff0c$$a=\\frac{\\Delta v}{\\Delta t}=\\omega^2r$$\uff1b
\n\u2463<\/strong>\u4e5f\u53ef\u4ee5\u7528\u6b63\u5f26\u8fd1\u4f3c\u6c42\u5f26\u957f\uff0c$$l=2rsin(\\frac{\\omega\\Delta t}{2})\\approx r \\omega\\Delta t$$\uff1b
\n\u2464<\/strong>\u5f53\u7136\u5b8c\u5168\u53ef\u4ee5\u5728\u77e2\u91cf\u4e09\u89d2\u5f62\u4e2d\u76f4\u63a5\u6c42\u89e3\uff0c$$sin(\\frac{\\omega \\Delta t}{2})=\\frac{\\frac{1}{2}\\Delta v}{v}$$\uff0c$$\\frac{\\Delta v}{\\Delta t}=\\omega v$$…
\n\u2465<\/strong>\u5728\u77e2\u91cf\u4e09\u89d2\u5f62\u4e2d\u7528\u4f59\u5f26\u5b9a\u7406\uff0c
\n$$\\Delta{v}=\\sqrt{2v^2-2v^2cos(\\omega\\Delta t)}=\\sqrt{2}v\\sqrt{1-cos(\\omega\\Delta t)}=\\sqrt{2}v\\sqrt{2sin^2\\frac{\\omega\\Delta t}{2}}=2vsin\\frac{\\omega\\Delta t}{2}$$
\n$$\\Delta v=v\\omega\\Delta t$$\uff0c$$\\frac{\\Delta v}{\\Delta t}=v\\omega$$…<\/p>\n
\u548c\u524d\u9762\u4e0d\u540c\uff0c\u53e6\u4e00\u4e2a\u601d\u8def\u662f\u4ece\u8fd0\u52a8\u53e0\u52a0\u7684\u89d2\u5ea6\u63a8\u5bfc\u5411\u5fc3\u52a0\u901f\u5ea6\uff1a \u2469<\/strong>\u7528\u901f\u5ea6\u77e2\u91cf\u7684\u6b63\u4ea4\u5206\u89e3\u53ef\u5173\u8054\u5230\u7b80\u8c10\u632f\u52a8\uff0c$$v_x=\\omega r cos(\\omega t)$$\uff0c$$v_y=-\\omega r sin(\\omega t)$$\uff0c\u5206\u522b\u5bf9\u65f6\u95f4\u6c42\u5bfc\u5f97$$a_x=-\\omega^2 r sin(\\omega t)$$\uff0c$$a_y=-\\omega^2 r cos(\\omega t)$$\uff0c$$a=\\sqrt{a_x^2+a_y^2}$$\uff0c\u548c\u901a\u5e38\u7684\u6781\u9650\u6cd5\u5206\u6790$$\\Delta v$$\u5411\u5fc3\u4e0d\u540c\uff0c\u8fd9\u91cc\u53ef\u4ee5\u76f4\u63a5\u5f97\u51fa\u52a0\u901f\u5ea6\u65b9\u5411\u6307\u5411\u5706\u5fc3\u7684\u7ed3\u8bba\u3002<\/p>\n \u91cd\u65b0\u6574\u7406\u4e86\u8fd9\u4e9b\u5bf9\u5e94\u8bd5\u7684\u610f\u4e49\u4e0d\u5927\uff0c\u9664\u4e86\u987a\u4fbf\u7528\u4e00\u4e0b\u7269\u7406\u4e2d\u5076\u5c14\u7528\u5230\u7684\u8fd1\u4f3c\u8ba1\u7b97\uff0c\u5927\u591a\u6570\u5b66\u751f\u53ea\u5173\u5fc3\u7ed3\u8bba\u5c31\u53ef\u4ee5\u5e94\u4ed8\u4e86\uff0c\u4f46\u5bf9\u77e5\u8bc6\u8ba4\u77e5\u7684\u5c42\u6b21\u662f\u4e0d\u540c\u7684\u3002\u901a\u5e38\u7684\u4e2d\u5b66\u7269\u7406\u6559\u5b66\uff0c\u4e0d\u4ec5\u5bf9\u79ef\u5206\u548c\u5bfc\u6570\u7684\u5e94\u7528\u8fc7\u5206\u5ef6\u540e\uff0c\u5bf9\u5411\u91cf\uff08\u77e2\u91cf\uff09\u7684\u8fd0\u7b97\u66f4\u662f\u8131\u8282\uff0c\u800c\u4e14\u610f\u8bc6\u4e0a\u7684\u91cd\u89c6\u660e\u663e\u4e0d\u591f\u3002<\/p>\n \u7f8e\u56fd\u79d1\u5b66\u4fc3\u8fdb\u4f1a(AAAS)1985\u5e74\u542f\u52a82061\u8ba1\u5212\uff08\u54c8\u96f7\u5f57\u661f2061\u5e74\u4f1a\u518d\u6b21\u5149\u4e34\u5730\u7403\uff09\uff0c\u5e2e\u52a9\u7f8e\u56fd\u4eba\u63d0\u9ad8\u79d1\u5b66\u3001\u6570\u5b66\u53ca\u6280\u672f\u7d20\u517b\uff0c\u201c\u7f8e\u56fd\u5386\u53f2\u4e0a\u6700\u663e\u8457\u7684\u79d1\u5b66\u6559\u80b2\u6539\u9769\u4e4b\u4e00\u201d\u2028\uff0c\u53f7\u79f0\u201c\u7ec8\u6781\u7684\u79d1\u5b66\u8ba1\u5212\u201d\u2028\u3002\u201c\u65e2\u7136\u6570\u5b66\u5bf9\u7406\u89e3\u81ea\u7136\u79d1\u5b66\u7b49\u5177\u6709\u4e2d\u5fc3\u91cd\u8981\u5730\u4f4d\uff0c\u56e0\u800c\u6211\u4eec\u518d\u6b21\u5f3a\u8c03\u9700\u8981\u628a\u6570\u5b66\u4e0e\u8fd9\u4e9b\u5b66\u79d1\u4ee5\u7efc\u5408\u7684\u65b9\u5f0f\u53bb\u6559\u3002\u7efc\u5408\u7684\u65b9\u6cd5\u8868\u660e\uff0c\u4e00\u4e2a\u73b0\u8c61\u7684\u6570\u5b66\u63cf\u8ff0\u5177\u6709\u9610\u660e\u548c\u52a0\u5f3a\u7684\u6548\u679c\u3002\u201d<\/p><\/blockquote>\n \u76f4\u63a5\u7528\u52a0\u901f\u5ea6\u662f\u4f4d\u7f6e\u77e2\u91cf\u5173\u4e8e\u65f6\u95f4\u7684\u4e8c\u9636\u5bfc\u6570\u8fd0\u7b97\u4e0d\u9999\u5417\uff1f\u6709\u65f6\u66f4\u4e00\u822c\u7684\u65b9\u6cd5\u53cd\u800c\u4f1a\u964d\u4f4e\u8ba4\u77e5\u96be\u5ea6\u3002 \u7279\u5730\u627e\u5230\u6768\u632f\u5b81\u6f14\u8bb2\u7684\u539f\u89c6\u9891\u622a\u53d6\u4e86\u5173\u4e8e\u5411\u5fc3\u52a0\u901f\u5ea6\u7684\u4e00\u6bb5\u3002\u56e0\u4e3a\u6218\u4e71\u7b49\u539f\u56e0\uff0c\u6570\u5b66\u6559\u6388\u7684\u513f\u5b50\u4e5f\u6ca1\u6709\u5b66\u8fc7\u9ad8\u4e2d\u7269\u7406\uff0c\u4f46\u4f3c\u4e4e\u4e0d\u59a8\u788d\u4ed6\u65e5\u540e\u5728\u7269\u7406\u5b66\u4e0a\u7684\u8d21\u732e\u3002\u800c\u73b0\u5728\u7684\u5c0f\u670b\u53cb\u4f3c\u4e4e\u5b66\u7684\u6709\u70b9\u591a…
\n\u2466<\/strong>\u8fd9\u91cc\u53ef\u4ee5\u987a\u4fbf\u7ec3\u4e60\u4e00\u4e0b\u4f59\u5f26\u7684\u8fd1\u4f3c\u8ba1\u7b97\uff0c$$\\frac{r}{cos(\\omega \\Delta t)}-r=\\frac{1}{2}a\\Delta t^2$$\uff0c$$cos(\\omega \\Delta t)\\approx 1-\\frac{(\\omega \\Delta t)^2}{2}$$\uff0c$$\\frac{1}{2}a\\Delta t^2=r\\frac{\\frac{1}{2}\\omega^2\\Delta t^2}{1-\\frac{1}{2}\\omega^2\\Delta t^2}$$…
\n\u2467<\/strong>\u540c\u6837\u662f\u8fd0\u52a8\u53e0\u52a0\uff0c\u7528\u52fe\u80a1\u5b9a\u7406\u8fd1\u4f3c\u8ba1\u7b97\u4e5f\u53ef\uff0c$$\\frac{1}{2}a\\Delta t^2=\\sqrt{r^2+(v\\Delta t)^2}-r$$\uff0c\u7b80\u5316\u5904\u7406\uff0c$$\\frac{1}{2}a\\Delta t^2=\\frac{(\\sqrt{r^2+(v\\Delta t)^2}-r)(\\sqrt{r^2+(v\\Delta t)^2}+r)}{\\sqrt{r^2+(v\\Delta t)^2}+r}=\\frac{v^2\\Delta t^2}{\\sqrt{r^2+(v\\Delta t)^2}+r}$$\uff0c$$\\frac{1}{2}a=\\frac{v^2}{2r}$$…
\n\u2468<\/strong>\u5bf9\u4e8e\u4e0a\u9762\u7684\u5904\u7406\uff0c\u5b59\u6d5a\u8c6a\u540c\u5b66\u662f\u7528\u79fb\u9879\u540e\u5e73\u65b9\uff0c\u9ad8\u9636\u65e0\u7a77\u5c0f\u91cf\u6d88\u9879\u3002$$\\frac{1}{2}a\\Delta t^2+r=\\sqrt{r^2+(v\\Delta t)^2}$$\uff0c$$ar\\Delta t^2+r^2+(\\frac{1}{2}a\\Delta t^2)^2=r^2+v^2\\Delta t^2$$\uff0c$$ar=v^2$$<\/p>\n
\n$$sin\\theta=\\frac{y}{r}$$\uff0c$$cos\\theta=\\frac{x}{r}$$
\n$$\\vec{v}=vsin\\theta \\hat{x}-vcos\\theta \\hat{y}=v\\frac{y}{r}\\hat{x}-v\\frac{x}{r}\\hat{y}$$
\n$$\\vec{a}=\\frac{d\\vec{v}}{dt}$$\uff0c$$\\vec{a}=\\frac{v}{r}(v_y\\hat{x}-v_x\\hat{y})$$
\n$$\\left|\\vec{a}\\right|=\\frac{v}{r}\\sqrt{v_x^2+v_y^2}=\\frac{v^2}{r}$$
\n\u66f4\u4e00\u822c\uff1a
\n$$\\vec{r}(t)=rcos\\theta(t)\\hat{x}+rsin\\theta(t)\\hat{y}$$
\n$$\\vec{v}=\\frac{d\\vec{r}}{dt}=r(-sin\\theta(t))\\frac{d\\theta}{dt}\\hat{x}+rcos\\theta(t)\\frac{d\\theta}{dt}\\hat{y}$$
\n\u5bf9\u4e8e\u7b49\u901f\u5706\u5468\u8fd0\u52a8\uff0c$$\\frac{d\\theta}{dt}=\\omega=const.$$
\n$$\\vec{v}=\\omega r(-sin\\theta(t))\\hat{x}+rcos\\theta(t)\\hat{y}$$
\n$$\\vec{a}=\\frac{d\\vec{v}}{dt}=-\\omega^2 r(cos\\theta(t))\\hat{x}+sin\\theta(t)\\hat{y}$$
\n$$\\left|\\vec{a}\\right|=\\omega^2 r$$
\n\u524d\u9762\u662f\u5bf9\u5411\u5fc3\u52a0\u901f\u5ea6\u7684\u63a8\u5bfc\uff0c\u800c\u5bf9\u5b83\u7684\u7406\u89e3\u5927\u591a\u5c40\u9650\u5728\u76f4\u63a5\u5e94\u7528\u7684\u5c42\u9762\uff0c\u5728FloatHeadPhysics\u9891\u9053\u4e0a\u770b\u5230\u66f4\u76f4\u89c2\u7684\u903b\u8f91\uff1a
\n\u534a\u5f84\u4e0d\u53d8\u901f\u5ea6\u52a0\u500d\uff0c\u76f8\u540c\u4e24\u4e2a\u4f4d\u7f6e\u7684\u901f\u5ea6\u53d8\u5316\u91cf\u540c\u6837\u52a0\u500d\uff0c\u800c\u6240\u9700\u8981\u65f6\u95f4\u5219\u56e0\u4e3a\u901f\u5ea6\u52a0\u500d\u800c\u51cf\u534a\uff0c\u6240\u4ee5\u901f\u5ea6\u53d8\u5316\u91cf\u5e94\u8be5\u662f\u5e73\u65b9\u500d\uff1b\u540c\u7406\uff0c\u901f\u5ea6\u4e0d\u53d8\u534a\u5f84\u52a0\u500d\uff0c\u76f8\u540c\u4f4d\u7f6e\uff08\u89d2\u5ea6\uff09\u7684\u901f\u5ea6\u53d8\u5316\u91cf\u4e0d\u53d8\uff0c\u800c\u7531\u4e8e\u5f27\u957f\u52a0\u500d\u901f\u5ea6\u4e0d\u53d8\uff0c\u6240\u9700\u65f6\u95f4\u52a0\u500d\uff0c\u90a3\u901f\u5ea6\u53d8\u5316\u7387\u51cf\u534a\u3002<\/em><\/p>\n
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