[高中物理竞赛辅导参考资料之04角动量守恒定律与刚体的定轴转动.ppt

转动惯量的计算 M b = I 将刚体转动定律 与质点运动定律 F = a m 对比 转动惯量 是刚体转动惯性的量度 I I ∑ 与刚体的质量、形状、大小及质量对转轴的分布情况有关 质量连续分布的刚体用积分求 I 为体积元 处的密度 I I 的单位为 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 分立质点的算例 可视为分立质点结构的刚体 转轴 若连接两小球（视为质点）的轻细硬杆的质量可以忽略，则 ∑ 转轴 ∑ 0.75 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 直棒算例 质量连续分布的刚体 匀直细杆对中垂轴的 匀直细杆对端垂轴的 质心 新轴 质心轴 平行移轴定理 对新轴的转动惯量 对质心轴的转动惯量 新轴对心轴的平移量 例如： 时 代入可得 端 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 圆盘算例 匀质薄圆盘对心垂轴的 取半径为 微宽为 的窄环带的质量为质元 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 球体算例 匀质实心球对心轴的 可看成是许多半径不同的共轴薄圆盘的转动惯量 的迭加 距 为 、半径为 、微厚为 的薄圆盘的转动惯量为 其中 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 常用结果 L R m m 匀质薄圆盘 匀质细直棒 转轴通过中心垂直盘面 2 2 I = m R 1 2 3 I = m L 1 转轴通过端点与棒垂直 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 其它典型 匀质矩形薄板 转轴通过中心垂直板面 I = (a + b ) 2 2 m 12 匀质细圆环 转轴通过中心垂直环面 I = m R