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<HTML><HEAD><TITLE>new</TITLE><META content="text/html; charset=gb2312" http-equiv=Content-Type><LINK href="text.css" rel=stylesheet type=text/css><META content="Microsoft FrontPage 4.0" name=GENERATOR></HEAD><body leftmargin="15"><center><b><br>2 动量矩定理</b></center> <table border="0" cellpadding="0" cellspacing="0" width="560"> <tr> <td width="20"><b><font color="#0000FF">一、</font></b></td> <td width="540"><b><font color="#0000FF">质点的动量矩定理</font><font color="#800000">（对定点）</font></b></td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>牛二定律:</td> <td><img border="0" src="pic1/3053_217.GIF" width="63" height="27"></td> <td><img border="0" src="pic1/3053_218.GIF" width="129" height="50"></td> </tr> </table> </td> <td width="50%" rowspan="3"> <p align="center"><img border="0" src="pic1/3053_219.GIF" width="217" height="157"></td> </tr> <tr> <td width="50%"><img border="0" src="pic1/3053_220.GIF" width="178" height="50"></td> </tr> <tr> <td width="50%"><img border="0" src="pic1/3053_221.GIF" width="252" height="50"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><img border="0" src="pic1/3053_222.GIF" width="178" height="50"></td> <td> <img border="0" src="pic1/3053_223.GIF" width="183" height="50"></td> <td> →<b>微分形式</b></td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td> 或 </td> <td><img border="0" src="pic1/3053_224.GIF" width="150" height="31"></td> </tr> </table> </td> <td><img border="0" src="pic1/3053_225.GIF" width="263" height="32"></td> <td>→<font color="#800000">冲量矩</font></td> </tr> <tr> <td> <p align="right"><font color="#800000">元冲量 </font></td> <td> <p align="center"><b>积分形式（有限形式）</b></td> <td></td> </tr> </table> </td> </tr> <tr> <td width="20"><b><font color="#0000FF">二、</font></b></td> <td width="540"><b><font color="#0000FF">质点系的动量矩定理</font></b><font color="#800000"><b>（对定点）</b></font></td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>任意质点： </td> <td><img border="0" src="pic1/3053_226.GIF" width="253" height="48"></td> <td> 且 </td> <td><img border="0" src="pic1/3053_227.GIF" width="109" height="31"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><img border="0" src="pic1/3053_228.GIF" width="27" height="22"></td> <td> <b>微分形式：</b> </td> <td><img border="0" src="pic1/3053_229.GIF" width="134" height="51"></td> <td> 对定点 </td> <td><img border="0" src="pic1/3053_230.GIF" width="130" height="48"></td> <td> 对定轴 </td> </tr> <tr> <td></td> <td> <p align="center">或</td> <td><img border="0" src="pic1/3053_231.GIF" width="139" height="31"></td> <td></td> <td></td> <td></td> </tr> <tr> <td><img border="0" src="pic1/3053_228.GIF" width="27" height="22"></td> <td> <b>积分形式：</b> </td> <td><img border="0" src="pic1/3053_232.GIF" width="169" height="31"></td> <td></td> <td></td> <td></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="1" cellpadding="0" cellspacing="0" bordercolor="#008080"> <tr> <td>问题：动量矩定理可求什么量？求几个？用何种方程？</td> </tr> </table> </td> </tr> <tr> <td width="20"><b><font color="#0000FF">三、</font></b></td> <td width="540"><b><font color="#0000FF">平面运动刚体的动量矩定理（对质心，对瞬心）（书上没有）</font></b></td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><font color="#0000FF">1.对质心</font></td> <td width="50%" rowspan="4"> <p align="center"><img border="0" src="pic1/3053_233.GIF" width="202" height="157"></td> </tr> <tr> <td width="50%"><img border="0" src="pic1/3053_234.GIF" width="133" height="50"></td> </tr> <tr> <td width="50%">（此式成立，不证）</td> </tr> <tr> <td width="50%"><img border="0" src="pic1/3053_235.GIF" width="186" height="31"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><font color="#0000FF">2. 对瞬心的两种情况：</font></td> <td width="50%" rowspan="4"> <p align="center"><img border="0" src="pic1/3053_236.GIF" width="281" height="160"></td> </tr> <tr> <td width="50%"><img border="0" src="pic1/3053_237.GIF" width="130" height="30"></td> </tr> <tr> <td width="50%"> <table border="1" cellpadding="0" cellspacing="0" bordercolor="#008080"> <tr> <td><font color="#FF0000">特别注意：</font><br> 该关系仅仅对瞬心的这两种情况成立，对其它情况的瞬心一般不成立。</td> </tr> </table> </td> </tr> <tr> <td width="50%"><b>解题步骤：</b></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540">(一)取研究对象（取分离体）；<br> (二)画受力图、运动图（只画外力、不画内力）；<br> (三)列解方程。</td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><b>例1</b><font color="#800000">（例5-1，用动量矩定理求解）</font></td> <td width="50%" align="center" rowspan="3"><img border="0" src="pic1/3053_238.GIF" width="249" height="188"></td> </tr> <tr> <td width="50%">图示系统。<br> 均质滚子A、滑轮B重量和半径均为Q和r，滚子纯滚动，三角块固定不动，重为G，倾角为α，重物重量P。求:<br> ①滚子质心的加速度aC ；<br> ②地面给三角块的反力偶。</td> </tr> <tr> <td width="50%">（动量定理中未能求；这两问均可用动量矩定理求）</td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><b>例2</b><font color="#800000">（P204，例5-12，欧拉涡轮方程，在流体力学中的应用）</font></td> <td width="50%" rowspan="3"> <p align="center"><img border="0" src="pic1/3053_239.GIF" width="296" height="154"></td> </tr> <tr> <td width="50%">已知水在涡轮机中的流动情况，求水对涡轮机的转动力矩（欧拉涡轮方程）。</td> </tr> <tr> <td width="50%"><img border="0" src="pic1/3053_240.GIF" width="238" height="26"></td> </tr> </table> </td> </tr> <tr> <td width="20"><b><font color="#0000FF">四、</font></b></td> <td width="540"><b><font color="#0000FF">动量矩守恒定律</font></b></td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><b>动量矩定理微分形式:</b> </td> <td><img border="0" src="pic1/3053_241.GIF" width="134" height="51"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td rowspan="2"><img border="0" src="pic1/3053_242.GIF" width="38" height="43"> </td> <td> <img border="0" src="pic1/3053_243.GIF" width="112" height="31"> </td> <td> <img border="0" src="pic1/3053_244.GIF" width="126" height="29"> </td> <td> ——质点系对定点O动量矩守恒</td> </tr> <tr> <td> <img border="0" src="pic1/3053_245.GIF" width="110" height="30"> </td> <td> <img border="0" src="pic1/3053_246.GIF" width="111" height="24"> </td> <td> ——质点系对定轴 z 动量矩守恒</td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><b>例3</b><font color="#800000">（P208 例5-15，动量矩守恒）</font></td> <td width="50%" rowspan="8"> <p align="center"><img border="0" src="pic1/3053_247.GIF" width="181" height="281"></td> </tr> <tr> <td width="50%">图示系统。<br> 质量为m1 = 5kg，半径r = 30cm的均质圆盘，可绕铅直轴 z 转动，在圆盘中心用铰链D连接一质量m<font size="1">2</font> = 4kg的均质细杆AB，AB = 2r，可绕D转动。<br> 当AB杆在铅直位置时，圆盘的角速度为ω = 90rpm。<br> 试求杆转到水平位置，碰到销钉C而相对静止时，圆盘的角速度。</td> </tr> <tr> <td width="50%"> </td> </tr> <tr> <td width="50%"> </td> </tr> <tr> <td width="50%"> </td> </tr> <tr> <td width="50%"> </td> </tr> <tr> <td width="50%"> </td> </tr> <tr> <td width="50%"> </td> </tr> </table> </td> </tr> <tr> <td width="560" colspan="2"> <p align="center"> <a href="3053_1.htm"><font color="#FF6666">[ 上一节 ]</font></a> <a href="3053_3.htm"><font color="#00CC00">[ 下一节 ]</font></a> </td> </tr> </table> </BODY></HTML> ⌨️ 快捷键说明
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