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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 刚体的转动惯量</b></center> <table border="0" cellpadding="0" cellspacing="0" width="560"> <tr> <td width="20"></td> <td width="540">我们知道，质量是质点惯性的度量。</td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td bgcolor="#FF00FF"> <table border="0" cellspacing="1"> <tr> <td bgcolor="#FFFFFF">问题①： 对质点系，质量是什么的度量？</td> </tr> </table> </td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540">——质系随质心平动惯性的度量。当质系不受任何外力时，其质心保持匀速直线运动。</td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellspacing="0" cellpadding="0"> <tr> <td bgcolor="#FF00FF"> <table border="0" cellspacing="1"> <tr> <td bgcolor="#FFFFFF">问题②： <br> 对转动刚体，如无外力偶，将保持匀速转动，即其有“转动惯性”，如何度量其转动惯性？</td> </tr> </table> </td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540">——刚体对轴的转动惯量。</td> </tr> <tr> <td width="20"><font color="#0000FF"><b>一、</b></font></td> <td width="540"><b><font color="#0000FF">刚体对轴的转动惯量</font></b></td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellspacing="0" width="100%" cellpadding="0"> <tr> <td width="50%">刚体对（z）轴的<b>转动惯量</b>：</td> <td width="50%" rowspan="5"> <p align="center"><img border="0" src="pic/3042.h18.gif" width="190" height="171"></td> </tr> <tr> <td width="50%"><img border="0" src="pic/3042.h19.gif" width="135" height="30"></td> </tr> <tr> <td width="50%">其中ρ<font size="1">z</font>是刚体对(z)轴的<b>回转半径（惯性半径）</b></td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>连续体表达式：</td> <td><img border="0" src="pic/3042.h20.gif" width="87" height="37"></td> </tr> </table> </td> </tr> <tr> <td width="50%">直角坐标下刚体对(z)轴的<b>转动惯量</b>：</td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"><img border="0" src="pic/3042.h21.gif" width="147" height="33"></td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>此时连续体表达式：</td> <td><img border="0" src="pic/3042.h22.gif" width="162" height="40"></td> </tr> </table> </td> </tr> <tr> <td width="20"><font color="#0000FF"><b>二、</b></font></td> <td width="540"><b><font color="#0000FF">刚体对点的极转动惯量</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%"><img border="0" src="pic/3042.h23.gif" width="249" height="32"></td> <td width="50%" rowspan="4"> <p align="center"><img border="0" src="pic/3042.h24.gif" width="209" height="154"></td> </tr> <tr> <td width="50%">连续体写法：</td> </tr> <tr> <td width="50%"><img border="0" src="pic/3042.h25.gif" width="194" height="39"></td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>可证：</td> <td><img border="0" src="pic/3042.h26.gif" width="159" height="49"></td> </tr> </table> </td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>对平板：</td> <td><img border="0" src="pic/3042.h27.gif" width="95" height="32"></td> </tr> </table> </td> </tr> <tr> <td width="20"><font color="#0000FF"><b>三、</b></font></td> <td width="540"><b><font color="#0000FF">平行轴定理</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%"> <p align="center"><img border="0" src="pic/3042.h28.gif" width="176" height="160"></td> <td width="50%"><img border="0" src="pic/3042.h29.gif" width="127" height="40"></td> </tr> </table> </td> </tr> <tr> <td width="20"><font color="#0000FF"><b>四、</b></font></td> <td width="540"><font color="#0000FF"><b>刚体转动惯量的求法 </b></font><font color="#FF6699">类似求重心方法，有以下几种。</font></td> </tr> <tr> <td width="20"></td> <td width="540"><u>1. 直接积分法</u></td> </tr> <tr> <td width="20"></td> <td width="540">对连续刚体，由定义积分求。有时用到极转动惯量的概念。</td> </tr> <tr> <td width="20"></td> <td width="540"><b>常见规则图形刚体的转动惯量：</b>（其余见附录1 P404）</td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="34%" align="center">①均质细长杆：</td> <td width="33%" align="center">②均质圆盘：</td> <td width="33%" align="center" rowspan="3"><img border="0" src="pic/3042.h30.gif" width="144" height="156"></td> </tr> <tr> <td width="34%" align="center"><img border="0" src="pic/3042.h31.gif" width="198" height="63"></td> <td width="33%" align="center"><img border="0" src="pic/3042.h32.gif" width="89" height="48"></td> </tr> <tr> <td width="34%" align="center"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><img border="0" src="pic/3042.h33.gif" width="91" height="48"></td> <td><img border="0" src="pic/3042.h34.gif" width="82" height="48"></td> </tr> </table> </td> <td width="33%" align="center"><img border="0" src="pic/3042.h35.gif" width="116" height="48"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"><u>2. 组合法</u></td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>利用平行轴定理和</td> <td><img border="0" src="pic/3042.h36.gif" width="79" height="31"></td> <td>来求。对挖去部分，可令其转动惯量为负。</td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"><u>3. 实验法</u></td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%" colspan="2"> <p align="center">利用振动方程</td> <td width="50%"> <p align="center">利用刚体转动微分方程</td> </tr> <tr> <td width="50%" colspan="2"> <p align="center"><img border="0" src="pic/3042.h37.gif" width="134" height="13"></td> <td width="50%"> <p align="center"><img border="0" src="pic/3042.h38.gif" width="134" height="13"></td> </tr> <tr> <td width="25%" align="center">① 扭振法</td> <td width="25%" align="center">② 摆振法</td> <td width="50%" align="center">③ 落体法（P241 题5-32）</td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"></td> </tr> <tr> <td width="560" colspan="2"> <p align="center"> <a href="3041.htm"><font color="#FF6666">[ 上一节 ]</font></a> <a href="3051_1.htm"><font color="#00CC00">[ 下一节 ]</font></a> </td> </tr> </table> </BODY></HTML> ⌨️ 快捷键说明
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