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)動剛體的轉(zhuǎn)動4 1 剛體的定軸轉(zhuǎn)動剛體的定軸轉(zhuǎn)動 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)點間距離保持不變的特殊質(zhì)點組任意兩質(zhì)點間距離保持不變的特殊質(zhì)點組剛體的運(yùn)動形式：平動、轉(zhuǎn)動剛體的運(yùn)動形式：平動、轉(zhuǎn)動.剛體平動剛體平動 質(zhì)點運(yùn)動質(zhì)點運(yùn)動 平動：假設(shè)剛體中所有平動：假設(shè)剛體中所有點的運(yùn)動軌跡都保持完全相點的運(yùn)動軌跡都保持完全相同，或者說剛體內(nèi)任意兩點同，或者說剛體內(nèi)任意兩點間的連線總是平行于它們的間的連線總是平行于它們的初始位置間的連線初始位置間的連線.第四章第四章 剛體的轉(zhuǎn)動剛體的轉(zhuǎn)動4 1 剛體的定軸轉(zhuǎn)動剛體的定軸轉(zhuǎn)動 轉(zhuǎn)動：剛體中所有的點都繞同一直線做圓周運(yùn)轉(zhuǎn)動：剛體中所有的點都繞同一直線做圓周運(yùn)動動.轉(zhuǎn)動又分定軸轉(zhuǎn)動和非定軸轉(zhuǎn)動轉(zhuǎn)動又分定軸轉(zhuǎn)動和非定軸轉(zhuǎn)動.剛體的平面運(yùn)動剛體的平面運(yùn)動.第四章第四章 剛體的轉(zhuǎn)動剛體的轉(zhuǎn)動4 1 剛體的定軸轉(zhuǎn)動剛體的定軸轉(zhuǎn)動 剛體的一般運(yùn)動剛體的一般運(yùn)動 質(zhì)心的平動質(zhì)心的平動繞質(zhì)心的轉(zhuǎn)動繞質(zhì)心的轉(zhuǎn)動+第四章第四章 剛體的轉(zhuǎn)動剛體的轉(zhuǎn)動4 1 剛體的定軸轉(zhuǎn)動剛體的定軸轉(zhuǎn)動一一 剛體轉(zhuǎn)動的角速度和角加速度剛體轉(zhuǎn)動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約定約定沿逆時針方向轉(zhuǎn)動沿逆時針方向轉(zhuǎn)動 沿逆時針方向轉(zhuǎn)動沿逆時針方向轉(zhuǎn)動 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)動剛體的轉(zhuǎn)動4 1 剛體的定軸轉(zhuǎn)動剛體的定軸轉(zhuǎn)動角加速度角加速度1）每一質(zhì)點均作圓周運(yùn)動，圓面為轉(zhuǎn)動平面；每一質(zhì)點均作圓周運(yùn)動，圓面為轉(zhuǎn)動平面；2）任一質(zhì)點運(yùn)動任一質(zhì)點運(yùn)動 均相同，但均相同，但 不同；不同；3）運(yùn)動描述僅需一個坐標(biāo)運(yùn)動描述僅需一個坐標(biāo).定軸轉(zhuǎn)動的定軸轉(zhuǎn)動的特點特點 剛體定軸轉(zhuǎn)動一剛體定軸轉(zhuǎn)動一維轉(zhuǎn)動的轉(zhuǎn)動方向可維轉(zhuǎn)動的轉(zhuǎn)動方向可以用角速度的正負(fù)來表以用角速度的正負(fù)來表示示.第四章第四章 剛體的轉(zhuǎn)動剛體的轉(zhuǎn)動4 1 剛體的定軸轉(zhuǎn)動剛體的定軸轉(zhuǎn)動二二 勻變速轉(zhuǎn)動公式勻變速轉(zhuǎn)動公式 剛體剛體繞繞定軸作勻變速轉(zhuǎn)動定軸作勻變速轉(zhuǎn)動質(zhì)點質(zhì)點勻變速直線運(yùn)動勻變速直線運(yùn)動 當(dāng)剛體繞定軸轉(zhuǎn)動的角加速度為恒量時，剛體做當(dāng)剛體繞定軸轉(zhuǎn)動的角加速度為恒量時，剛體做勻變速轉(zhuǎn)動勻變速轉(zhuǎn)動.剛體勻變速轉(zhuǎn)動與質(zhì)點勻變速直線運(yùn)動公式比照剛體勻變速轉(zhuǎn)動與質(zhì)點勻變速直線運(yùn)動公式比照第四章第四章 剛體的轉(zhuǎn)動剛體的轉(zhuǎn)動4 1 剛體的定軸轉(zhuǎn)動剛體的定軸轉(zhuǎn)動三三 角量與線量的關(guān)系角量與線量的關(guān)系第四章第四章 剛體的轉(zhuǎn)動剛體的轉(zhuǎn)動4 1 剛體的定軸轉(zhuǎn)動剛體的定軸轉(zhuǎn)動飛輪飛輪 30 s 內(nèi)轉(zhuǎn)過的角度內(nèi)轉(zhuǎn)過的角度 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，因受制動而均勻減速，經(jīng)因受制動而均勻減速，經(jīng) 30 s 停止轉(zhuǎn)動停止轉(zhuǎn)動.試求：試求：1角加速度和在此時間內(nèi)飛輪所轉(zhuǎn)的圈數(shù)；角加速度和在此時間內(nèi)飛輪所轉(zhuǎn)的圈數(shù)；2制動制動開始后開始后 t=6 s 時飛輪的角速度；時飛輪的角速度；3t=6 s 時飛輪邊時飛輪邊緣上一點的線速度、切向加速度和法向加速度緣上一點的線速度、切向加速度和法向加速度.解解（1）t=30 s 時，時，設(shè)設(shè).飛輪做勻減速運(yùn)動飛輪做勻減速運(yùn)動時，時，t=0 s 第四章第四章 剛體的轉(zhuǎn)動剛體的轉(zhuǎn)動4 1 剛體的定軸轉(zhuǎn)動剛體的定軸轉(zhuǎn)動（2）時，飛輪的角速度時，飛輪的角速度（3）時，飛輪邊緣上一點的線速度大小時，飛輪邊緣上一點的線速度大小該點的切向加速度和法向加速度該點的切向加速度和法向加速度轉(zhuǎn)過的圈數(shù)轉(zhuǎn)過的圈數(shù)第四章第四章 剛體的轉(zhuǎn)動剛體的轉(zhuǎn)動4 1 剛體的定軸轉(zhuǎn)動剛體的定軸轉(zhuǎn)動 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中心的軸轉(zhuǎn)動繞垂直其橫截面通過中心的軸轉(zhuǎn)動.開始時，它的角速開始時，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)子的角加速度與時間成正比轉(zhuǎn)子的角加速度與時間成正比.問在這段時間內(nèi)，轉(zhuǎn)子問在這段時間內(nèi)，轉(zhuǎn)子轉(zhuǎn)過多少轉(zhuǎn)？轉(zhuǎn)過多少轉(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 時時所以所以第四章第四章 剛體的轉(zhuǎn)動剛體的轉(zhuǎn)動4 1 剛體的定軸轉(zhuǎn)動剛體的定軸轉(zhuǎn)動轉(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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