上頁(yè)下頁(yè)結(jié)束返回第五章角動(dòng)量關(guān)于對(duì)稱性5.25.2.1質(zhì)點(diǎn)系對(duì)參考點(diǎn)的角動(dòng)量定律及守恒律5.2.2質(zhì)點(diǎn)系對(duì)軸的角動(dòng)量定律及守恒律上頁(yè)下頁(yè)結(jié)束返回第五章角動(dòng)量關(guān)于對(duì)稱性5.25.2.1質(zhì)點(diǎn)系對(duì)參考點(diǎn)的角動(dòng)量定律及守恒律1.質(zhì)點(diǎn)系對(duì)參考點(diǎn)的角動(dòng)量對(duì)參考點(diǎn)對(duì)質(zhì)點(diǎn)系中的第i個(gè)質(zhì)點(diǎn),有上頁(yè)下頁(yè)結(jié)束返回第五章角動(dòng)量關(guān)于對(duì)稱性因質(zhì)點(diǎn)i與質(zhì)點(diǎn)j間的互相斥力關(guān)系為jiij且二力到參考點(diǎn)O的垂直距離相等，故成對(duì)出現(xiàn)的內(nèi)力對(duì)O點(diǎn)的扭矩矢量和為零.即上頁(yè)下頁(yè)結(jié)束返回第五章角動(dòng)量關(guān)于對(duì)稱性即質(zhì)點(diǎn)系對(duì)給定點(diǎn)(參考點(diǎn))的角動(dòng)量的時(shí)間變化率等于作用在體系上所有外力對(duì)該點(diǎn)扭力矢量和.即若外力對(duì)參考點(diǎn)的扭矩的矢量和仍然為零，則質(zhì)點(diǎn)系對(duì)該點(diǎn)的角動(dòng)量保持不變.上頁(yè)下頁(yè)結(jié)束返回第五章角動(dòng)量關(guān)于對(duì)稱性5.2.2質(zhì)點(diǎn)系對(duì)軸的角動(dòng)量定律及守恒律設(shè)質(zhì)點(diǎn)在垂直于z軸的平面內(nèi)運(yùn)動(dòng)，第i個(gè)質(zhì)點(diǎn)對(duì)z軸的角動(dòng)量1.質(zhì)點(diǎn)系對(duì)軸的角動(dòng)量質(zhì)點(diǎn)系對(duì)軸的角動(dòng)量2.質(zhì)點(diǎn)系對(duì)軸的角動(dòng)量定律質(zhì)點(diǎn)在垂直于z軸的平面內(nèi)運(yùn)動(dòng)，第i個(gè)質(zhì)點(diǎn)上頁(yè)下頁(yè)結(jié)束返回第五章角動(dòng)量關(guān)于對(duì)稱性——稱質(zhì)點(diǎn)系對(duì)z軸的角動(dòng)量定律.上頁(yè)下頁(yè)結(jié)束返回第五章角動(dòng)量關(guān)于對(duì)稱性3.質(zhì)點(diǎn)系對(duì)軸的角動(dòng)量守恒定理sin若質(zhì)點(diǎn)系各質(zhì)點(diǎn)繞z作圓周運(yùn)動(dòng)諸如茹可夫斯基凳，花樣溜冰等.討論上頁(yè)下頁(yè)結(jié)束返回第五章角動(dòng)量關(guān)于對(duì)稱性[例題]裝置如圖所示.滑輪兩旁懸掛的重物與盤的質(zhì)量相同而處于平衡，現(xiàn)有距盤底高為h質(zhì)量為m的膠泥自由下落，求膠泥粘在盤上時(shí)盤獲得到初速率.滑輪和繩質(zhì)量不計(jì).不計(jì)軸承磨擦及繩的伸長(zhǎng).上頁(yè)下頁(yè)結(jié)束返回第五章角動(dòng)量關(guān)于對(duì)稱性gh重物和膠泥視為質(zhì)點(diǎn)系，繩的拉力及物體所受重力為外力.因不計(jì)滑輪、繩質(zhì)量及軸承磨擦，兩側(cè)繩的拉力相等；重物與盤所受重力也相等.它們對(duì)軸心O的扭力之和為零，故質(zhì)點(diǎn)系所受外力對(duì)O點(diǎn)的扭力之和就等于膠泥的重扭力，不等于零.但在碰撞時(shí)質(zhì)點(diǎn)系的動(dòng)量定理，膠泥與盤之間的碰撞內(nèi)力對(duì)O點(diǎn)的扭矩遠(yuǎn)小于外扭力之和質(zhì)點(diǎn)系的動(dòng)量定理，即內(nèi)扭矩對(duì)質(zhì)點(diǎn)系內(nèi)各質(zhì)點(diǎn)運(yùn)動(dòng)的影響遠(yuǎn)小于外扭矩的影響.論質(zhì)點(diǎn)系內(nèi)各質(zhì)點(diǎn)的運(yùn)動(dòng)時(shí)，可不計(jì)外扭力.故在碰撞時(shí)，可用質(zhì)點(diǎn)系對(duì)O軸角動(dòng)量守恒多項(xiàng)式求近似解.直于屏幕向外方向?yàn)镺軸正方向，有上頁(yè)下頁(yè)結(jié)束返回第五章角動(dòng)量關(guān)于對(duì)稱性本題也可以借助對(duì)點(diǎn)的角動(dòng)量守恒求解.
