《2动量定理.pptVIP

例题11-2. 在图示系统中,均质杆OA、AB与均质轮的质量均为m,OA杆的长度为l1,AB杆的长度为l2,轮的半径为R,轮沿水平面作纯滚动.在图示瞬时,OA杆的角速度为?,求整个系统的动量. 解:系统由三个物体组成. 解:取小车,沙箱和重物组成的系统为研究对象 * 　　§ 11-1　动量与冲量 　　§ 11-2　动量定理 　　例题 　　§ 11-3　质心运动定理 　　例题 　　返回 第十一章　动量定理 动力学 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. § 11-1　动量与冲量 (1)动量: P = m v 矢量性;瞬时性;相对性 (2)冲量: I = F t dI = F dt Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. (1)质点的动量定理: 微分形式: dP = Fdt 积分形式: (2)守恒定理: 若 F= 0 则 P = c (恒矢量) 若 Fx= 0 则 Px = c (恒量) § 11-2　动量定理 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. (3)质点系的动量定理 [1] 动量: P = ? mi vi 质心: 质心速度: P = M vc Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. [2] 动量定理: 设质点系有n个质点,第i个质点的质量为mi 速度为vi ;外界物体对该质点作用的外力为Fi(e) ,质点系内其它质点对该质点作用的内力为Fi(i) .则有: R(i) = ?Fi(i) = 0 dPi = Fi(e)dt + Fi(i)dt = dIi(e) + dIi(i) 积分形式: P2 - P1 = I(e) 微分形式: dP = R(e)dt Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 应用合矢量投影定理可将上两式投影到任一轴上. 若 R(e) = 0 则 P = c (恒矢量) 若 R(e)x = 0 则 Px = c (恒量) 由上述可知:内力的主矢R(i) = ?Fi(i) = 0即内力对质点系的动量无影响;而外力的主矢则影响质点系动量,即影响质心速度的变化. [3]守恒定理: Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 11-3.质心运动定理 (1)运动定理: M ac = R(e) (2)守恒定理: 若 R(e) = 0 则 vc = c (恒矢量) 若 R(e)x = 0 则 vcx = c (恒量) Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 例题11-1. 图示椭圆规尺AB的质量为 2m1 ,曲柄OC的质量为m1 ,而滑块A和B的质量均为m2.已知OC=AC=CB=l ,曲柄和尺的质心分别在其中点上,曲柄绕O轴转动的角速度?为常量.求图示瞬时系统的动量. O B ? C A ?t Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 解:系统由四个物体组成. 滑块A和B的质心与椭圆规尺A