剛體在外力作用下,形狀和大小都不發(fā)生變化的物體 . （任7

第四章第四章 剛體的轉(zhuǎn)動(dòng)剛體的轉(zhuǎn)動(dòng)4 1 剛體的定軸轉(zhuǎn)動(dòng)剛體的定軸轉(zhuǎn)動(dòng) 剛體：在外力作用下，形狀和大小都不發(fā)生變化剛體：在外力作用下，形狀和大小都不發(fā)生變化的物體的物體.任意兩質(zhì)點(diǎn)間距離保持不變的特殊質(zhì)點(diǎn)組任意兩質(zhì)點(diǎn)間距離保持不變的特殊質(zhì)點(diǎn)組剛體的運(yùn)動(dòng)形式：平動(dòng)、轉(zhuǎn)動(dòng)剛體的運(yùn)動(dòng)形式：平動(dòng)、轉(zhuǎn)動(dòng).剛體平動(dòng)剛體平動(dòng) 質(zhì)點(diǎn)運(yùn)動(dòng)質(zhì)點(diǎn)運(yùn)動(dòng) 平動(dòng)：假設(shè)剛體中所有平動(dòng)：假設(shè)剛體中所有點(diǎn)的運(yùn)動(dòng)軌跡都保持完全相點(diǎn)的運(yùn)動(dòng)軌跡都保持完全相同，或者說(shuō)剛體內(nèi)任意兩點(diǎn)同，或者說(shuō)剛體內(nèi)任意兩點(diǎn)間的連線(xiàn)總是平行于它們的間的連線(xiàn)總是平行于它們的初始位置間的連線(xiàn)初始位置間的連線(xiàn).第四章第四章 剛體的轉(zhuǎn)動(dòng)剛體的轉(zhuǎn)動(dòng)4 1 剛體的定軸轉(zhuǎn)動(dòng)剛體的定軸轉(zhuǎn)動(dòng) 轉(zhuǎn)動(dòng)：剛體中所有的點(diǎn)都繞同一直線(xiàn)做圓周運(yùn)轉(zhuǎn)動(dòng)：剛體中所有的點(diǎn)都繞同一直線(xiàn)做圓周運(yùn)動(dòng)動(dòng).轉(zhuǎn)動(dòng)又分定軸轉(zhuǎn)動(dòng)和非定軸轉(zhuǎn)動(dòng)轉(zhuǎn)動(dòng)又分定軸轉(zhuǎn)動(dòng)和非定軸轉(zhuǎn)動(dòng).剛體的平面運(yùn)動(dòng)剛體的平面運(yùn)動(dòng).第四章第四章 剛體的轉(zhuǎn)動(dòng)剛體的轉(zhuǎn)動(dòng)4 1 剛體的定軸轉(zhuǎn)動(dòng)剛體的定軸轉(zhuǎn)動(dòng) 剛體的一般運(yùn)動(dòng)剛體的一般運(yùn)動(dòng) 質(zhì)心的平動(dòng)質(zhì)心的平動(dòng)繞質(zhì)心的轉(zhuǎn)動(dòng)繞質(zhì)心的轉(zhuǎn)動(dòng)+第四章第四章 剛體的轉(zhuǎn)動(dòng)剛體的轉(zhuǎn)動(dòng)4 1 剛體的定軸轉(zhuǎn)動(dòng)剛體的定軸轉(zhuǎn)動(dòng)一一 剛體轉(zhuǎn)動(dòng)的角速度和角加速度剛體轉(zhuǎn)動(dòng)的角速度和角加速度參考平面參考平面角位移角位移 角坐標(biāo)角坐標(biāo)q約定約定沿逆時(shí)針?lè)较蜣D(zhuǎn)動(dòng)沿逆時(shí)針?lè)较蜣D(zhuǎn)動(dòng) 沿逆時(shí)針?lè)较蜣D(zhuǎn)動(dòng)沿逆時(shí)針?lè)较蜣D(zhuǎn)動(dòng) 角速度矢量角速度矢量 方向方向:右手右手螺旋方向螺旋方向參考軸參考軸第四章第四章 剛體的轉(zhuǎn)動(dòng)剛體的轉(zhuǎn)動(dòng)4 1 剛體的定軸轉(zhuǎn)動(dòng)剛體的定軸轉(zhuǎn)動(dòng)角加速度角加速度1）每一質(zhì)點(diǎn)均作圓周運(yùn)動(dòng)，圓面為轉(zhuǎn)動(dòng)平面；每一質(zhì)點(diǎn)均作圓周運(yùn)動(dòng)，圓面為轉(zhuǎn)動(dòng)平面；2）任一質(zhì)點(diǎn)運(yùn)動(dòng)任一質(zhì)點(diǎn)運(yùn)動(dòng) 均相同，但均相同，但 不同；不同；3）運(yùn)動(dòng)描述僅需一個(gè)坐標(biāo)運(yùn)動(dòng)描述僅需一個(gè)坐標(biāo).定軸轉(zhuǎn)動(dòng)的定軸轉(zhuǎn)動(dòng)的特點(diǎn)特點(diǎn) 剛體定軸轉(zhuǎn)動(dòng)一剛體定軸轉(zhuǎn)動(dòng)一維轉(zhuǎn)動(dòng)的轉(zhuǎn)動(dòng)方向可維轉(zhuǎn)動(dòng)的轉(zhuǎn)動(dòng)方向可以用角速度的正負(fù)來(lái)表以用角速度的正負(fù)來(lái)表示示.第四章第四章 剛體的轉(zhuǎn)動(dòng)剛體的轉(zhuǎn)動(dòng)4 1 剛體的定軸轉(zhuǎn)動(dòng)剛體的定軸轉(zhuǎn)動(dòng)二二 勻變速轉(zhuǎn)動(dòng)公式勻變速轉(zhuǎn)動(dòng)公式 剛體剛體繞繞定軸作勻變速轉(zhuǎn)動(dòng)定軸作勻變速轉(zhuǎn)動(dòng)質(zhì)點(diǎn)質(zhì)點(diǎn)勻變速直線(xiàn)運(yùn)動(dòng)勻變速直線(xiàn)運(yùn)動(dòng) 當(dāng)剛體繞定軸轉(zhuǎn)動(dòng)的角加速度為恒量時(shí)，剛體做當(dāng)剛體繞定軸轉(zhuǎn)動(dòng)的角加速度為恒量時(shí)，剛體做勻變速轉(zhuǎn)動(dòng)勻變速轉(zhuǎn)動(dòng).剛體勻變速轉(zhuǎn)動(dòng)與質(zhì)點(diǎn)勻變速直線(xiàn)運(yùn)動(dòng)公式比照剛體勻變速轉(zhuǎn)動(dòng)與質(zhì)點(diǎn)勻變速直線(xiàn)運(yùn)動(dòng)公式比照第四章第四章 剛體的轉(zhuǎn)動(dòng)剛體的轉(zhuǎn)動(dòng)4 1 剛體的定軸轉(zhuǎn)動(dòng)剛體的定軸轉(zhuǎn)動(dòng)三三 角量與線(xiàn)量的關(guān)系角量與線(xiàn)量的關(guān)系第四章第四章 剛體的轉(zhuǎn)動(dòng)剛體的轉(zhuǎn)動(dòng)4 1 剛體的定軸轉(zhuǎn)動(dòng)剛體的定軸轉(zhuǎn)動(dòng)飛輪飛輪 30 s 內(nèi)轉(zhuǎn)過(guò)的角度內(nèi)轉(zhuǎn)過(guò)的角度 例例1 一飛輪半徑為一飛輪半徑為 0.2m、轉(zhuǎn)速為轉(zhuǎn)速為150rmin-1，因受制動(dòng)而均勻減速，經(jīng)因受制動(dòng)而均勻減速，經(jīng) 30 s 停止轉(zhuǎn)動(dòng)停止轉(zhuǎn)動(dòng).試求：試求：1角加速度和在此時(shí)間內(nèi)飛輪所轉(zhuǎn)的圈數(shù)；角加速度和在此時(shí)間內(nèi)飛輪所轉(zhuǎn)的圈數(shù)；2制動(dòng)制動(dòng)開(kāi)始后開(kāi)始后 t=6 s 時(shí)飛輪的角速度；時(shí)飛輪的角速度；3t=6 s 時(shí)飛輪邊時(shí)飛輪邊緣上一點(diǎn)的線(xiàn)速度、切向加速度和法向加速度緣上一點(diǎn)的線(xiàn)速度、切向加速度和法向加速度.解解（1）t=30 s 時(shí)，時(shí)，設(shè)設(shè).飛輪做勻減速運(yùn)動(dòng)飛輪做勻減速運(yùn)動(dòng)時(shí)，時(shí)，t=0 s 第四章第四章 剛體的轉(zhuǎn)動(dòng)剛體的轉(zhuǎn)動(dòng)4 1 剛體的定軸轉(zhuǎn)動(dòng)剛體的定軸轉(zhuǎn)動(dòng)（2）時(shí)，飛輪的角速度時(shí)，飛輪的角速度（3）時(shí)，飛輪邊緣上一點(diǎn)的線(xiàn)速度大小時(shí)，飛輪邊緣上一點(diǎn)的線(xiàn)速度大小該點(diǎn)的切向加速度和法向加速度該點(diǎn)的切向加速度和法向加速度轉(zhuǎn)過(guò)的圈數(shù)轉(zhuǎn)過(guò)的圈數(shù)第四章第四章 剛體的轉(zhuǎn)動(dòng)剛體的轉(zhuǎn)動(dòng)4 1 剛體的定軸轉(zhuǎn)動(dòng)剛體的定軸轉(zhuǎn)動(dòng) 例例2 在高速旋轉(zhuǎn)的微型電機(jī)里，有一圓柱形轉(zhuǎn)子可在高速旋轉(zhuǎn)的微型電機(jī)里，有一圓柱形轉(zhuǎn)子可繞垂直其橫截面通過(guò)中心的軸轉(zhuǎn)動(dòng)繞垂直其橫截面通過(guò)中心的軸轉(zhuǎn)動(dòng).開(kāi)始時(shí)，它的角速開(kāi)始時(shí)，它的角速度度 ，經(jīng)，經(jīng)300s 后，其轉(zhuǎn)速達(dá)到后，其轉(zhuǎn)速達(dá)到 18000rmin-1.已知已知轉(zhuǎn)子的角加速度與時(shí)間成正比轉(zhuǎn)子的角加速度與時(shí)間成正比.問(wèn)在這段時(shí)間內(nèi)，轉(zhuǎn)子問(wèn)在這段時(shí)間內(nèi)，轉(zhuǎn)子轉(zhuǎn)過(guò)多少轉(zhuǎn)？轉(zhuǎn)過(guò)多少轉(zhuǎn)？解解 由題意，令由題意，令 ，即，即 ，積分，積分 得得當(dāng)當(dāng)t=300s 時(shí)時(shí)所以所以第四章第四章 剛體的轉(zhuǎn)動(dòng)剛體的轉(zhuǎn)動(dòng)4 1 剛體的定軸轉(zhuǎn)動(dòng)剛體的定軸轉(zhuǎn)動(dòng)轉(zhuǎn)子的角速度轉(zhuǎn)子的角速度由角速度的定義由角速度的定義得得有有在在 300 s 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