1、2020/9/6,Ocean University of China,1,2-5 角動量 角動量守恒定律,2-5-1 質(zhì)點的角動量,質(zhì)點的角動量,質(zhì)點對O的角動量：,x,y,z,O,2020/9/6,Ocean University of China,2,2-5 角動量 角動量守恒定律,2-5-1 質(zhì)點的角動量,質(zhì)點的角動量,2020/9/6,Ocean University of China,3,2-5 角動量 角動量守恒定律,2-5-1 質(zhì)點的角動量,作圓周運動的質(zhì)點的角動量,O,2020/9/6,Ocean University of China,4,2-5 角動量 角動量守恒定律,2-

2、5-2 質(zhì)點的角動量定理,2020/9/6,Ocean University of China,5,2-5 角動量 角動量守恒定律,2-5-2 質(zhì)點的角動量定理,令：,力矩,質(zhì)點角動量定理,2020/9/6,Ocean University of China,6,2-5 角動量 角動量守恒定律,2-5-3 質(zhì)點的角動量守恒定律定理,=0,If,We have:,質(zhì)點所受外力對固定點的力矩為零，則質(zhì)點對該固定點的角動量守恒。 質(zhì)點的角動量守恒定律。,2020/9/6,Ocean University of China,7,2-6 剛體的定軸轉(zhuǎn)動,2-6-2 質(zhì)點系的角動量定理,質(zhì)點系的對固定點角

3、動量定理,2020/9/6,Ocean University of China,8,2-6 剛體的定軸轉(zhuǎn)動,2-6-2 質(zhì)點系的角動量定理,如果某一質(zhì)點系中的所有點都繞固定軸在與軸垂直的平面內(nèi)運動，則位置矢量的z軸分量對該點在z軸上的角動量分量沒有影響：,2020/9/6,Ocean University of China,9,2-6 剛體的定軸轉(zhuǎn)動,2-6-2 質(zhì)點系的角動量定理,同樣道理，如果某一質(zhì)點系中的所有點都繞固定軸在與軸垂直的平面內(nèi)運動，則外力的z軸分量對該外力在z軸上的力矩分量沒有影響：,2020/9/6,Ocean University of China,10,2-6 剛體的定

4、軸轉(zhuǎn)動,2-6-2 質(zhì)點系對軸的角動量定理,2020/9/6,Ocean University of China,11,2-6 剛體的定軸轉(zhuǎn)動,2-6-2 質(zhì)點系對軸的角動量定理,如果質(zhì)點角速度相同：,轉(zhuǎn)動慣量,2020/9/6,Ocean University of China,12,2-6 剛體的定軸轉(zhuǎn)動,2-6-2 質(zhì)點系對軸的角動量定理,如果質(zhì)點角速度相同：,聯(lián)系一下力和動量的關(guān)系：,2020/9/6,Ocean University of China,13,2-6 剛體的定軸轉(zhuǎn)動,2-6-2 定軸轉(zhuǎn)動質(zhì)點系的轉(zhuǎn)動慣量,質(zhì)點系的轉(zhuǎn)動慣量,質(zhì)量分布與轉(zhuǎn)軸的位置。,單個質(zhì)點的轉(zhuǎn)動慣量,質(zhì)量

5、連續(xù)分布的剛體的轉(zhuǎn)動慣量,均為到轉(zhuǎn)動軸的垂直距離,2020/9/6,Ocean University of China,14,2-6 剛體的定軸轉(zhuǎn)動,2-6-3 剛體的轉(zhuǎn)動定律,剛體繞定軸轉(zhuǎn)動時，它的角加速度與作用于剛體上的合外力矩成正比，與剛體對轉(zhuǎn)軸的轉(zhuǎn)動慣量成反比。,剛體定軸轉(zhuǎn)動的轉(zhuǎn)動定律：,2020/9/6,Ocean University of China,15,2-6 剛體的定軸轉(zhuǎn)動,2-6-3 剛體的轉(zhuǎn)動定律,剛體定軸轉(zhuǎn)動：,2020/9/6,Ocean University of China,16,Example:,R,2020/9/6,Ocean University of C

6、hina,17,Example:,R,2020/9/6,Ocean University of China,18,Example:,2020/9/6,Ocean University of China,19,Example:,2020/9/6,Ocean University of China,20,Example:,2020/9/6,Ocean University of China,21,2-6 剛體的定軸轉(zhuǎn)動,2-6-4 定軸轉(zhuǎn)動的動能定理,剛體的轉(zhuǎn)動動能,2020/9/6,Ocean University of China,22,2-6 剛體的定軸轉(zhuǎn)動,2-6-4 定軸轉(zhuǎn)動的動能定理,

7、力矩的功,2020/9/6,Ocean University of China,23,2-6 剛體的定軸轉(zhuǎn)動,2-6-4 定軸轉(zhuǎn)動的動能定理,定軸轉(zhuǎn)動的動能定理,合外力矩對定軸轉(zhuǎn)動剛體所做的功等于剛體轉(zhuǎn)動動能的增量,2020/9/6,Ocean University of China,24,Example:,2020/9/6,Ocean University of China,25,Example:,2020/9/6,Ocean University of China,26,2-6 剛體的定軸轉(zhuǎn)動,2-6-5 剛體組對軸的角動量定理及其守恒定律,定軸轉(zhuǎn)動剛體的角動量的增量等于合外力矩的沖量矩。

8、,2020/9/6,Ocean University of China,27,2-6 剛體的定軸轉(zhuǎn)動,2-6-5 剛體組對軸的角動量定理及其守恒定律,外力對某軸的力矩之和為零，則該物體對同一軸的角動量守恒。,對軸的角動量守恒定律：,2020/9/6,Ocean University of China,28,2-6 剛體的定軸轉(zhuǎn)動,2-6- 5 剛體組對軸的角動量定理及其守恒定律,角動量守恒定律的兩種情況：,1、轉(zhuǎn)動慣量保持不變的剛體,例：,2、轉(zhuǎn)動慣量可變的物體,例：,2020/9/6,Ocean University of China,29,圓錐擺,Discussion,分析系統(tǒng)守恒性質(zhì),2

9、020/9/6,Ocean University of China,30,圓錐擺,Discussion,2020/9/6,Ocean University of China,31,Example:,如圖，長為l，質(zhì)量為M的均勻細(xì)棒可饒過O點的轉(zhuǎn)軸在豎直面內(nèi)自由轉(zhuǎn)動。一質(zhì)量為m的質(zhì)點以初速v0沿水平方向運動，與靜止在豎直位置的細(xì)棒的末端發(fā)生完全非彈性碰撞，碰撞后兩者一起上擺。求 （1）碰撞后瞬間兩者一起上擺的角速度， （2）兩者一起上擺的最大角度 。,2020/9/6,Ocean University of China,32,Example:,2020/9/6,Ocean University of China,33,Example:,2020/9/6,Ocean University of China,34,Example:,2020/9/6,Ocean University of China,35,Example:,如圖，長為l，質(zhì)量為M的均勻細(xì)棒可饒過O點的轉(zhuǎn)軸在豎直面內(nèi)自由轉(zhuǎn)動。一質(zhì)量為m的質(zhì)點以初速v0沿水平方向運動，與靜止在豎直位置的細(xì)棒的末端發(fā)生完全彈性碰撞。