大學(xué)物理角動(dòng)量和力矩

1、ch3,review,質(zhì)心 質(zhì)心坐標(biāo) 質(zhì)心速度 質(zhì)心加速度,表示質(zhì)點(diǎn)系的質(zhì)量分布的中心位置,代表質(zhì)點(diǎn)系的總動(dòng)量,代表質(zhì)點(diǎn)系的合外力 描述質(zhì)點(diǎn)系的平移軌跡,ch3,質(zhì)點(diǎn)系的動(dòng)能 克尼希定理,碰撞 動(dòng)量守恒,質(zhì)點(diǎn)系的總動(dòng)能等于相對(duì)于質(zhì)心系的動(dòng)能加上隨質(zhì)心整體平移的動(dòng)能，即,兩質(zhì)點(diǎn)體系的動(dòng)能,ch4,第四章 角動(dòng)量守恒,4-1 質(zhì)點(diǎn)的角動(dòng)量,1.引入,2）觀察質(zhì)點(diǎn)的勻速直線運(yùn)動(dòng):質(zhì)點(diǎn)相對(duì)于參考點(diǎn)的掠面速度不變,動(dòng)量、動(dòng)能都不能對(duì)上述現(xiàn)象作出統(tǒng)一描述，需要引入新的物理量,1）開(kāi)普勒：若以太陽(yáng) 為中心，行星的位置矢量在相等時(shí)間內(nèi)掃過(guò)(sweep through)相等的面積,ch4,2.質(zhì)點(diǎn)對(duì)參考點(diǎn)的角動(dòng)

2、量 (angular momentum,what counts for angular momentum is not how fast it is going away from the origin, but how much it is going around the origin,描述質(zhì)點(diǎn)的運(yùn)動(dòng)方向相對(duì)于參考點(diǎn)的變化或物體的轉(zhuǎn)動(dòng)特征的物理量,angular momentum depends upon the position of the axis abour which it is to be calculated,ch4,3.質(zhì)點(diǎn)對(duì)z軸的角動(dòng)量,是l到z軸的角,可以在z軸上任意找

3、一點(diǎn)，求出質(zhì)點(diǎn)對(duì)該點(diǎn)的角動(dòng)量，再求z軸分量,ch4,一、力矩和質(zhì)點(diǎn)的角動(dòng)量定理,4-2 力矩和角動(dòng)量定理,1.力矩 (torque,2.質(zhì)點(diǎn)的角動(dòng)量定理：質(zhì)點(diǎn)對(duì)任一固定點(diǎn)的角動(dòng)量的時(shí)間變化率，等于外力對(duì)該點(diǎn)的力矩,力對(duì)某點(diǎn)的力矩,單位：nm,ch4,例題4.1圓錐擺由一根長(zhǎng)為l的繩子懸掛著一個(gè)質(zhì)量為m的作勻速圓周運(yùn)動(dòng)的小球構(gòu)成。若擺線與鉛垂線成 角，試求擺球的速率,研究對(duì)象：圓錐擺 參考系：實(shí)驗(yàn)室 選擇參考點(diǎn)：支點(diǎn)o 受力與運(yùn)動(dòng)分析,ch4,速度調(diào)節(jié)器,ch4,二、質(zhì)點(diǎn)系的角動(dòng)量定理,1.質(zhì)點(diǎn)系角動(dòng)量隨時(shí)間的變化率,2.質(zhì)點(diǎn)系對(duì)固定點(diǎn)的總內(nèi)力矩為零,3.質(zhì)點(diǎn)系的角動(dòng)量定理,the rate c

4、hange of the totle angular momentum about any axis is equal to the external torque about that axis,慣性系中成立,ch4,4.角動(dòng)量守恒定律（普遍的,如果質(zhì)點(diǎn)系所受到的總外力矩為零 ，則質(zhì)點(diǎn)系的角動(dòng)量守恒,if no external torques act upon a system of particles, the angular momentum remains costant,質(zhì)點(diǎn)系對(duì)慣性系中某給定參考點(diǎn)的角動(dòng)量的時(shí)間變化率，等于作用在該質(zhì)點(diǎn)系上所有外力對(duì)該給定參考點(diǎn)的總力矩,ch4,5.幾種特殊情況,有心力場(chǎng)中的質(zhì)點(diǎn)（系）對(duì)“心”的角動(dòng)量總是守恒的,質(zhì)點(diǎn)系的重力的合力矩可集中到質(zhì)心處理,ch4,6. 守恒條件,角動(dòng)量守恒：合外力對(duì)固定點(diǎn)的力矩為零 與參考系、研究系統(tǒng)和參考點(diǎn)都有關(guān)系,動(dòng)量守恒：合外力為零 與參考系和研究系統(tǒng)有關(guān)系,保守系機(jī)械能守恒：合外力作功為零 與參考系和研究系統(tǒng)有關(guān)系,ch4,三、質(zhì)心系的角動(dòng)量定理,對(duì)質(zhì)心角動(dòng)量+隨質(zhì)心角動(dòng)量,質(zhì)心系的角動(dòng)量定理,角動(dòng)量定理對(duì)慣性系成立，但站在質(zhì)心系上時(shí)，無(wú)論其是否是慣性系，則角動(dòng)量定理形式上仍成立,ch4,只受重力作用的質(zhì)點(diǎn)系對(duì)質(zhì)心的角動(dòng)量守恒,ch4,例題4.2質(zhì)量為m1和m2的兩個(gè)質(zhì)點(diǎn)的位